Necessary packages

library(tidyverse)
library(FIELDimageR)
library(raster)
library(readxl)
library(gsheet)
library(foreach)
library(agricolae)
library(reshape2)
library(cowplot)
library(gbm)
library(lime)
library(lme4)
library(DescTools)
library(factoextra)
library(FactoMineR)
library(corrplot)
library(magick)
library(patchwork)
library(forcats)
library(ggdist)

Example of RGB indices for one image

Load pictures names

pics<-list.files("./pics/01-Calonectria_leaf_bligth")
length(pics)
## [1] 300
# write(pics, "pics_names.txt")

List of RGB-based spectral indices to be calculated in the image

# Vegetation indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")

Load a single image

#Choose one image to prepare the pipeline
EX.L1<-stack(paste("./pics/01-Calonectria_leaf_bligth/",pics[254],sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot =T)
## [1] "3 layers available"

# plotRGB(EX.L.Shape)
EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Blue"), plot = T)
## [1] "3 layers available"

plot(EX1.Indices$Blue)

hist(EX1.Indices$Blue)

mask

# EX.L2<-fieldMask(mosaic=EX.L1, myIndex = "Red", cropValue=200, cropAbove=T, plot = T)
# EX.L2<-fieldMask(mosaic=EX.L1, index = "BI", cropValue=1, cropAbove=F, plot = T)
EX.L2<-fieldMask(mosaic=EX.L1, myIndex = c("Blue"), cropValue=175, cropAbove=T, plot = T)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"

# plotRGB(EX.L2$newMosaic)
plotRGB(EX.L2$newMosaic)

class(EX.L2$mask)
## [1] "RasterStack"
## attr(,"package")
## [1] "raster"
rgb_fig = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_void()+
  coord_fixed()
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
cut = mask(EX.L1, EX.L2$newMosaic)
plot(cut)

EX.L4<-fieldIndex(mosaic=cut,
                  index = index)
## [1] "3 layers available"

plot(EX.L4$BGI)

gli_fig = as.data.frame(EX.L4$BGI, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = BGI))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_void()+
  coord_fixed()
plot_grid(rgb_fig, gli_fig, axis = "b",
          rel_widths = c(0.9,1),
          labels = c("RGB", "BGI"),
          scale = 0.90)

# ggsave("figs/leaf_gli.png",dpi = 600, height = 3, width =10 )
df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  gather(1:(3+length(index)), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[30])
## `summarise()` ungrouping output (override with `.groups` argument)

Wheat leaf blast

pics<-list.files("./pics/01-Wheat_leaf_blast")
# length(pics)
#indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")


box = data.frame()

for(i in 1:length(pics)){

EX.L1<-stack(paste("./pics/01-Wheat_leaf_blast/",pics[i],sep = ""))
EX.L1<-aggregate(EX.L1, fact=10)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)

EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=180, cropAbove=T, plot = F)

cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)


df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  mutate(gray = 0.299*Red+0.587*Green+0.114*Blue) %>% 
  gather(c(1:(3+length(index)),15), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  dplyr::summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[i])


box = box %>% 
  bind_rows(dff)}
length(unique(box$leaf))
write.table(box,"data/indexes_WLB.txt")
box = read.table("data/indexes_WLB.txt")

Load severity data

# sev_data = gsheet2tbl("https://docs.google.com/spreadsheets/d/106sg_O8DeALZpWnxERQNgk8UKgsFbhobWwrl4JXOzbo/edit#gid=0")


sev = gsheet2tbl("https://docs.google.com/spreadsheets/d/106sg_O8DeALZpWnxERQNgk8UKgsFbhobWwrl4JXOzbo/edit#gid=0")
sev
## # A tibble: 200 x 5
##    inoculated   code    rep pic_name   sev
##    <chr>        <chr> <dbl> <chr>    <dbl>
##  1 BRS Guamirim 42        1 G_42_R1   0.18
##  2 BRS Guamirim 42        2 G_42_R2   0.38
##  3 BRS Guamirim 42        3 G_42_R3   0   
##  4 BRS Guamirim 42        4 G_42_R4   0.05
##  5 BRS Guamirim 108       1 G_108_R1  0.2 
##  6 BRS Guamirim 108       2 G_108_R2  0.9 
##  7 BRS Guamirim 108       3 G_108_R3  0.28
##  8 BRS Guamirim 108       4 G_108_R4  0.14
##  9 BRS Guamirim 110       1 G_110_R1  0.19
## 10 BRS Guamirim 110       2 G_110_R2  0.21
## # ... with 190 more rows
blast_data = gsheet2tbl("https://docs.google.com/spreadsheets/d/1KnJ9N8jqKPMjCt8jCLv7OqYL9hLyYeK8wkGEBmlGSVI/edit?usp=sharing") %>% 
  dplyr::select(code, city, region, position_wheat, host,species)
# blast_data

sev_data = full_join(sev, blast_data, by = "code") %>% 
  mutate(n = seq(1:1123)) %>% 
  filter(n<201) %>% 
  dplyr::select(-n) %>% 
  
  dplyr::select(pic_name, sev)
# sev_data


length(unique(sev$pic_name))
## [1] 200
all_data = box %>%
  separate(leaf, into = c("pic_name", "jpg"), sep = ".jpg") %>%
  # separate(pic_name, into = c("hh", "isolate","repp"), sep = "_", remove = F) %>%
  dplyr::select(-jpg) %>% 
  full_join(sev_data) %>% 
  # filter(sev>0) %>% 
  mutate(sev = case_when(sev==0 ~0.01,
                         sev >0 ~sev)) %>% 
  filter(!is.na(index)) %>% 
  mutate(sev = sev)
## Joining, by = "pic_name"
length(unique(all_data$pic_name))
## [1] 200
# length(unique(box$leaf))
summary(sev$sev)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.6375 49.6250 44.0737 76.0050 99.9300

Images

hist_sev_WLB =  sev %>% 
  ggplot(aes(sev))+
  geom_histogram(color = "white", fill = "black", bins = 20)+
  theme_minimal_hgrid(font_size = 10)+
  labs(x = "Severity (%)",
       y = "Frequency")+
  scale_x_continuous(limits = c(-5,105), breaks = seq(0,100,25))+
  # theme_void()+
  # coord_fixed()+
  theme(panel.background = element_rect(color = "black"),
        axis.title.y = element_text(size=8))
hist_sev_WLB
## Warning: Removed 2 rows containing missing values (geom_bar).

EX.L1<-stack(paste("./pics/01-Wheat_leaf_blast/","G_758_R2.jpg",sep = ""))
EX.L1<-aggregate(EX.L1, fact=10)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)
## [1] "3 layers available"
EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)
## [1] "3 layers available"
EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=180, cropAbove=T, plot = F)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)
## [1] "3 layers available"
# plot(EX.L4$NGRDI)
rgb_fig_wlb = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"))
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
gli_fig_wlb = as.data.frame(EX.L4$VARI, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = VARI))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"),
        legend.title = element_text(size = 8),
        legend.text = element_text(size = 8))
# plot_grid(rgb_fig, gli_fig, axis = "b",
#           rel_widths = c(0.9,1),
#           labels = c("RGB", "NGRDI"),
#           scale = 0.90)

rgb_fig_wlb + gli_fig_wlb + hist_sev_WLB
## Warning: Removed 2 rows containing missing values (geom_bar).

# ggsave("figs/leaf_gli_wlb.png",dpi = 600, height = 4, width =12)

Relationship sev indices

rgb_gg = all_data %>% 
  filter(index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev, color = index)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =1)+
  scale_color_manual(values = c("steelblue","darkgreen", "darkred"))+
  theme_minimal_hgrid()+
  labs(x = "Mean value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))+
  theme(legend.position = "none")
rgb_gg
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

index_gg = all_data %>% 
  filter(!index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(color = "black", se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =2)+
  theme_minimal_hgrid()+
  labs(x = "Mean index value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))
index_gg
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plot_grid(
  plot_grid(NULL,rgb_gg,NULL, rel_widths =c(0.18,1,0.2), nrow = 1),
          index_gg,
          nrow = 2,
          rel_heights = c(0.5,1))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggsave("figs/index_sev_WLB.png", dpi = 500, height = 8, width = 10)
cor_wlb = all_data %>% 
  group_by(index) %>% 
  dplyr::summarise(cor = round(  cor.test(mean,sev, method = "spearman")$estimate,3),
                   P_value = cor.test(mean,sev, method = "spearman")$p.value) %>% 
  arrange(-cor)
## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties
## `summarise()` ungrouping output (override with `.groups` argument)
cor_wlb
## # A tibble: 13 x 3
##    index    cor  P_value
##    <chr>  <dbl>    <dbl>
##  1 SCI    0.867 1.14e-61
##  2 HI     0.823 1.70e-50
##  3 Blue   0.822 2.70e-50
##  4 HUE    0.752 9.44e-38
##  5 Red    0.666 5.11e-27
##  6 BI     0.643 1.12e-24
##  7 gray   0.59  4.16e-20
##  8 BGI    0.475 1.22e-12
##  9 Green  0.436 1.07e-10
## 10 SI     0.382 2.33e- 8
## 11 NGRDI -0.867 1.14e-61
## 12 VARI  -0.87  1.06e-62
## 13 GLI   -0.886 4.53e-68

Spread

all_data_spread = all_data %>% 
  # mutate(nn=1:length(all_data$pic_name)) %>% 
  pivot_wider(id_col = c(pic_name,sev),
              names_from = index, 
              values_from =  mean)   
all_data_spread
## # A tibble: 200 x 15
##    pic_name   sev   BGI    BI  Blue   GLI  gray Green       HI   HUE  NGRDI
##    <chr>    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>    <dbl> <dbl>  <dbl>
##  1 G_108_R1  0.2  0.535 107.   71.7 0.193  118.  131.  0.218   -1.56 0.0970
##  2 G_108_R2  0.9  0.646 103.   79.2 0.148  112.  122.  0.0459  -1.50 0.0872
##  3 G_108_R3  0.28 0.678  99.3  79.4 0.137  107.  116. -0.0920  -1.55 0.0858
##  4 G_108_R4  0.14 0.649 104.   79.8 0.148  112.  123. -0.0500  -1.56 0.0885
##  5 G_110_R1  0.19 0.651 102.   79.3 0.148  111.  122.  0.0730  -1.56 0.0903
##  6 G_110_R2  0.21 0.638 104.   79.1 0.151  113.  124.  0.0666  -1.56 0.0867
##  7 G_110_R3  0.3  0.645 107.   81.9 0.144  116.  127.  0.112   -1.56 0.0797
##  8 G_110_R4  0.08 0.694  98.1  79.7 0.133  105.  115. -0.164   -1.56 0.0887
##  9 G_112_R1  0.01 0.645 104.   80.1 0.150  113.  124. -0.00156 -1.56 0.0902
## 10 G_112_R2  0.06 0.690  99.4  80.5 0.134  107.  116. -0.170   -1.56 0.0874
## # ... with 190 more rows, and 4 more variables: Red <dbl>, SCI <dbl>, SI <dbl>,
## #   VARI <dbl>

GBM

train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.75*length(all_data_spread$sev),1))
# length(train)
gbm.fit = gbm(sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI,
             data = all_data_spread[train,],
             distribution = "gaussian",
              n.trees = 1000,
             interaction.depth = 3,
             shrinkage = 0.1,
             cv.folds = 5,
             n.cores = NULL, # will use all cores by default
             verbose = FALSE)
print(gbm.fit)
## gbm(formula = sev ~ BGI + BI + GLI + HI + HUE + NGRDI + VARI + 
##     gray + Red + Green + Blue + SI + SCI, distribution = "gaussian", 
##     data = all_data_spread[train, ], n.trees = 1000, interaction.depth = 3, 
##     shrinkage = 0.1, cv.folds = 5, verbose = FALSE, n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 1000 iterations were performed.
## The best cross-validation iteration was 52.
## There were 13 predictors of which 13 had non-zero influence.
sqrt(min(gbm.fit$cv.error))
## [1] 9.034891
gbm.perf(gbm.fit, method = "cv")

## [1] 52
# find index for n trees with minimum CV error
min_MSE <- which.min(gbm.fit$cv.error)
sqrt(gbm.fit$cv.error[min_MSE])
## [1] 9.034891
# best.iter <- gbm.perf(model1, method = "test")
# print(best.iter)

pred = predict(gbm.fit, newdata = all_data_spread[-train,-1], ntrees = 5000 )
## Using 52 trees...
sqrt(mean(((pred)-all_data_spread$sev[-train])^2))
## [1] 11.15379
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.9461264
plot((pred), (pred)-all_data_spread$sev[-train])
abline(a=0,b=0)

Testing various hyperparameters

Create hyperparameter grid

hyper_grid <- expand.grid(
  shrinkage = c(.001, .01, .1, .3),
  interaction.depth = c(1, 3, 5, 6),
  n.minobsinnode = c(5, 10, 15),
  bag.fraction = c(.5,.65, .8, 1), 
  optimal_trees = 0,               # a place to dump results
  min_RMSE = 0,
  CCC =0 # a place to dump results
)
# total number of combinations
nrow(hyper_grid)
## [1] 192
# randomize data
set.seed(1234)
train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.80*length(all_data_spread$sev),1))

# grid search 
for(i in 1:nrow(hyper_grid)) {

# reproducibility
set.seed(123)


 # train model
gbm.tune <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray +Red+Green+Blue + SI + SCI, #<<<<<
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = hyper_grid$interaction.depth[i],
  shrinkage = hyper_grid$shrinkage[i],
  n.minobsinnode = hyper_grid$n.minobsinnode[i],
  bag.fraction = hyper_grid$bag.fraction[i],
  train.fraction = .75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE)

pred = predict(gbm.tune, newdata = all_data_spread[-train,-1], ntrees = 5000 )
 # add min training error and trees to grid
  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$valid.error))
  hyper_grid$CCC[i] = CCC(pred, all_data_spread$sev[-train])$rho.c$est#<<<<<
  
}
## Using 5000 trees...
## Using 606 trees...
## Using 54 trees...
## Using 20 trees...
## Using 3601 trees...
## Using 323 trees...
## Using 29 trees...
## Using 9 trees...
## Using 3242 trees...
## Using 328 trees...
## Using 36 trees...
## Using 19 trees...
## Using 3225 trees...
## Using 331 trees...
## Using 39 trees...
## Using 7 trees...
## Using 4999 trees...
## Using 1013 trees...
## Using 58 trees...
## Using 31 trees...
## Using 3612 trees...
## Using 323 trees...
## Using 31 trees...
## Using 9 trees...
## Using 3378 trees...
## Using 328 trees...
## Using 31 trees...
## Using 71 trees...
## Using 3378 trees...
## Using 328 trees...
## Using 31 trees...
## Using 71 trees...
## Using 4999 trees...
## Using 945 trees...
## Using 91 trees...
## Using 23 trees...
## Using 4766 trees...
## Using 550 trees...
## Using 34 trees...
## Using 14 trees...
## Using 4766 trees...
## Using 550 trees...
## Using 34 trees...
## Using 14 trees...
## Using 4766 trees...
## Using 550 trees...
## Using 34 trees...
## Using 14 trees...
## Using 4995 trees...
## Using 591 trees...
## Using 50 trees...
## Using 27 trees...
## Using 3610 trees...
## Using 385 trees...
## Using 38 trees...
## Using 11 trees...
## Using 3304 trees...
## Using 5000 trees...
## Using 34 trees...
## Using 69 trees...
## Using 3205 trees...
## Using 4970 trees...
## Using 32 trees...
## Using 7 trees...
## Using 4995 trees...
## Using 938 trees...
## Using 2711 trees...
## Using 375 trees...
## Using 3493 trees...
## Using 336 trees...
## Using 31 trees...
## Using 53 trees...
## Using 3349 trees...
## Using 334 trees...
## Using 31 trees...
## Using 11 trees...
## Using 3349 trees...
## Using 324 trees...
## Using 31 trees...
## Using 11 trees...
## Using 4996 trees...
## Using 789 trees...
## Using 50 trees...
## Using 446 trees...
## Using 3659 trees...
## Using 389 trees...
## Using 38 trees...
## 
## Using 38 trees...
## Using 3659 trees...
## Using 389 trees...
## Using 38 trees...
## 
## Using 38 trees...
## Using 3659 trees...
## Using 389 trees...
## Using 38 trees...
## 
## Using 38 trees...
## Using 4999 trees...
## Using 739 trees...
## Using 91 trees...
## Using 27 trees...
## Using 3636 trees...
## Using 391 trees...
## Using 29 trees...
## Using 82 trees...
## Using 3606 trees...
## Using 4988 trees...
## Using 1606 trees...
## Using 70 trees...
## Using 3527 trees...
## Using 5000 trees...
## Using 1913 trees...
## Using 12 trees...
## Using 4999 trees...
## Using 739 trees...
## Using 54 trees...
## Using 27 trees...
## Using 3648 trees...
## Using 4999 trees...
## Using 4511 trees...
## Using 11 trees...
## Using 3653 trees...
## Using 4999 trees...
## Using 4985 trees...
## Using 13 trees...
## Using 3540 trees...
## Using 4967 trees...
## Using 4417 trees...
## Using 13 trees...
## Using 5000 trees...
## Using 630 trees...
## Using 3637 trees...
## Using 28 trees...
## Using 3450 trees...
## Using 336 trees...
## Using 29 trees...
## Using 12 trees...
## Using 3378 trees...
## Using 341 trees...
## Using 29 trees...
## Using 10 trees...
## Using 3378 trees...
## Using 341 trees...
## Using 29 trees...
## Using 10 trees...
## Using 5000 trees...
## Using 1017 trees...
## Using 122 trees...
## Using 130 trees...
## Using 4663 trees...
## Using 456 trees...
## Using 48 trees...
## Using 10 trees...
## Using 3029 trees...
## Using 378 trees...
## Using 35 trees...
## Using 9 trees...
## Using 3539 trees...
## Using 301 trees...
## Using 27 trees...
## Using 9 trees...
## Using 5000 trees...
## Using 4997 trees...
## Using 953 trees...
## Using 28 trees...
## Using 3651 trees...
## Using 5000 trees...
## Using 4990 trees...
## Using 4906 trees...
## Using 3384 trees...
## Using 337 trees...
## Using 5000 trees...
## Using 10 trees...
## Using 3367 trees...
## Using 343 trees...
## Using 33 trees...
## Using 142 trees...
## Using 4999 trees...
## Using 622 trees...
## Using 90 trees...
## Using 20 trees...
## Using 3456 trees...
## Using 350 trees...
## Using 43 trees...
## Using 13 trees...
## Using 3195 trees...
## Using 318 trees...
## Using 32 trees...
## Using 10 trees...
## Using 3220 trees...
## Using 320 trees...
## Using 31 trees...
## Using 10 trees...
best_par = hyper_grid %>% 
  dplyr::arrange(-CCC) %>%
  head(10)
best_par
##    shrinkage interaction.depth n.minobsinnode bag.fraction optimal_trees
## 1       0.01                 5              5         0.80          4988
## 2       0.10                 5              5         0.50            36
## 3       0.30                 5              5         0.50            19
## 4       0.01                 6              5         0.80          5000
## 5       0.30                 3             10         0.80            11
## 6       0.01                 6              5         0.50           331
## 7       0.01                 5              5         0.65          5000
## 8       0.01                 6              5         0.65          4970
## 9       0.10                 5             10         0.80          4985
## 10      0.30                 5             10         1.00            10
##    min_RMSE       CCC
## 1  10.83493 0.9731869
## 2  10.88780 0.9730593
## 3  11.04311 0.9729481
## 4  10.70554 0.9722267
## 5  10.84073 0.9716871
## 6  10.34085 0.9716634
## 7  10.62293 0.9713993
## 8  10.52067 0.9713708
## 9  10.54148 0.9711163
## 10 11.28268 0.9709846
# gbm.tune$fit

Best model

# for reproducibility
set.seed(123)

# train GBM model
gbm.fit.final <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+Red+Green+Blue+gray+SI+SCI,
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = best_par$optimal_trees[1],
  interaction.depth = best_par$interaction.depth[1],
  shrinkage = best_par$shrinkage[1],
  n.minobsinnode = best_par$n.minobsinnode[1],
  bag.fraction = best_par$bag.fraction[1], 
  train.fraction =0.75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE
  )

Relative influence

par(mar = c(5, 8, 1, 1))
summary_gbm_wlb = summary(
  gbm.fit.final, 
  cBars = 15,
  method = relative.influence, # also can use permutation.test.gbm
  las = 2
  )

rel_wlb = summary_gbm_wlb %>% 
  rownames_to_column("index") %>% 
  ggplot(aes(rel.inf, reorder(var, rel.inf)))+
  geom_col(aes(fill =rel.inf>1, color =rel.inf>1 ), width = 0.85)+
  theme_minimal_vgrid()+
  labs(x = "Relative influence (%)",
       y = "Model predictors",
       fill = "RI > 1%",
       color = "RI > 1%")
rel_wlb

ggsave("figs/var_influence.png",dpi = 600, height = 4, width = 6)

Partial dependence plots

gbm.fit.final %>%
  pdp::partial(pred.var = "NGRDI", n.trees = gbm.fit.final$n.trees, grid.resolution = 100) %>%
  ggplot(aes( NGRDI,(yhat)))+
  geom_line()

LIME

model_type.gbm <- function(x, ...) {
  return("regression")
}

predict_model.gbm <- function(x, newdata, ...) {
  pred <- predict(x, newdata, n.trees = x$n.trees)
  return(as.data.frame(pred))
}
# get a few observations to perform local interpretation on
local_obs <- (all_data_spread[-train,])[1:4, ]

# apply LIME
explainer <- lime(all_data_spread[train,], gbm.fit.final)
explanation <- lime::explain(local_obs, explainer, n_features = 7, n.trees =1)
plot_features(explanation)

Prediction

# predict values for test data
pred <- predict(gbm.fit.final,
                n.trees = gbm.fit.final$n.trees,
                all_data_spread[-train,])

# results
caret::RMSE((pred), all_data_spread[-train,]$sev)
## [1] 7.852842
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.9733397
cor((pred), all_data_spread$sev[-train])^2
## [1] 0.9491022
accuracy_wlb =data.frame(predi=pred, actual = all_data_spread$sev[-train]) %>% 
  summarise(RMSE = caret::RMSE(pred, actual),
            r = cor(pred, actual),
            s.shift = CCC(pred, actual)$s.shift,
            l.shift = CCC(pred, actual)$l.shift,
            C.b = CCC(pred, actual)$C.b,
            CCC = CCC(pred, actual)$rho.c$est,
            CIS = paste(
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[2],2),","," ",
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[3],2),sep = ""
  ))
accuracy_wlb
##       RMSE         r  s.shift    l.shift       C.b       CCC        CIS
## 1 7.852842 0.9742187 1.030742 0.02982214 0.9990977 0.9733397 0.95, 0.99

plot

# plot_grid(
conc_wlb = data.frame(predict = pred, actual =all_data_spread$sev[-train]) %>% 
ggplot(aes(actual,predict))+
  geom_point(size =2, color = "gray")+
  geom_abline(intercept = 0, slope= 1, size = .81, color = "black", linetype = "dashed")+
  geom_smooth(method = "lm", 
              color = "red",
              size =.81, se =F,
              fullrange=T)+
  theme_minimal_grid()+
  labs(x = "Predicted Severity (%)",
       y = "Actual Severity (%)")+
  coord_equal(xlim = c(0,100),
              ylim = c(0,100))+
  xlim(0,100)

ggsave("figs/concordance.png", dpi = 600, height = 3.5, width = 4)
## `geom_smooth()` using formula 'y ~ x'

Soybean Rust

pics<-list.files("./pics/01-soybean-rust-bg-blue")
# length(pics)
#indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")


box = data.frame()

for(i in 1:length(pics)){

EX.L1<-stack(paste("./pics/01-soybean-rust-bg-blue/",pics[i],sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)

EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=100, cropAbove=T, plot = F)

cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)


df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  mutate(gray = 0.299*Red+0.587*Green+0.114*Blue) %>% 
  gather(c(1:(3+length(index)),15), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  dplyr::summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[i])


box = box %>% 
  bind_rows(dff)}
length(unique(box$leaf))
write.table(box,"data/indexes_SBR.txt")
box = read.table("data/indexes_SBR.txt")

load SBR severity

sbr_load = gsheet2tbl("https://docs.google.com/spreadsheets/d/13TVKBQgfCAr7UGie_LHTF_kwPHC1XI_AkLKoRYtjPrQ/edit?usp=sharing")
all_data_sbr = box %>% 
  separate(leaf, into=c("file","format"), sep ="_") %>% 
  dplyr::select(-format) %>% 
  full_join(sbr_load) %>% 
  na.omit()
## Joining, by = "file"
length(unique(all_data_sbr$file))
## [1] 203
head(all_data_sbr)
##   index        mean         std        Q25         Q50         Q75       file
## 1   BGI   0.3997101  0.13599078  0.3234259   0.3843265   0.4506906 Ferrugem 1
## 2    BI  87.8460326 14.91203193 77.1221560  87.0969043  98.8352819 Ferrugem 1
## 3  Blue  41.0937912 11.80079235 33.5510204  40.1326531  46.7959184 Ferrugem 1
## 4   GLI   0.1959277  0.06355385  0.1562426   0.1952057   0.2354938 Ferrugem 1
## 5  gray  96.1659570 15.23897816 85.5722755  95.7584898 107.3897857 Ferrugem 1
## 6 Green 104.4390983 13.30553965 95.8163265 104.3571429 113.8163265 Ferrugem 1
##    sev
## 1 39.7
## 2 39.7
## 3 39.7
## 4 39.7
## 5 39.7
## 6 39.7
summary(all_data_sbr$sev)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.04    5.52   20.10   25.11   38.07   89.67

Images

hist_sev_sbr =  all_data_sbr %>%
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean) %>%
  ggplot(aes(sev))+
  geom_histogram(color = "white", fill = "black", bins = 20)+
  theme_minimal_hgrid(font_size = 10)+
  labs(x = "Severity (%)",
       y = "Frequency")+
  scale_x_continuous(limits = c(-5,105), breaks = seq(0,100,25))+
  # theme_void()+
  # coord_fixed()+
  theme(panel.background = element_rect(color = "black"),
        axis.title.y = element_text(size=8))
EX.L1<-stack(paste("./pics/01-soybean-rust-bg-blue/","Ferrugem 2_Median.jpg",sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)
## [1] "3 layers available"
EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)
## [1] "3 layers available"
EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=100, cropAbove=T, plot = F)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)
## [1] "3 layers available"
# plot(EX.L4$HUE)
rgb_fig_sbr = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"))
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
gli_fig_sbr = as.data.frame(EX.L4$HUE, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = HUE))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"),
        legend.title = element_text(size = 8),
        legend.text = element_text(size = 8))
rgb_fig_sbr + gli_fig_sbr + hist_sev_sbr #+
## Warning: Removed 2 rows containing missing values (geom_bar).

  # rgb_fig_wlb + gli_fig_wlb + hist_sev_WLB+
  #  plot_layout(widths = c(1, 1, 1),
  #              heights = c(1,1))

# ggsave("figs/leaf_gli.png",dpi = 600, height = 6, width =10)

Relationship sev indices

rgb_gg_sbr = all_data_sbr %>% 
  filter(index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev, color = index)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =1)+
  scale_color_manual(values = c("steelblue","darkgreen", "darkred"))+
  theme_minimal_hgrid()+
  labs(x = "Mean value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))+
  theme(legend.position = "none")
rgb_gg_sbr
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

index_gg_sbr = all_data_sbr %>% 
  filter(!index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(color = "black", se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =2)+
  theme_minimal_hgrid()+
  labs(x = "Mean index value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))
index_gg_sbr
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plot_grid(
  plot_grid(NULL,rgb_gg_sbr,NULL, rel_widths =c(0.18,1,0.2), nrow = 1),
          index_gg_sbr,
          nrow = 2,
          rel_heights = c(0.5,1))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggsave("figs/index_sev_SBR.png", dpi = 500, height = 8, width = 10)
cor_sbr = all_data_sbr %>% 
  group_by(index) %>% 
  dplyr::summarise(cor = round(  cor.test(mean,sev, method = "spearman")$estimate,3),
                   P_value = cor.test(mean,sev, method = "spearman")$p.value) %>% 
  arrange(-cor)
## `summarise()` ungrouping output (override with `.groups` argument)
cor_sbr
## # A tibble: 13 x 3
##    index    cor  P_value
##    <chr>  <dbl>    <dbl>
##  1 HUE    0.995 0.      
##  2 SCI    0.946 0.      
##  3 HI     0.906 0.      
##  4 Red    0.848 0.      
##  5 SI     0.823 0.      
##  6 BI     0.745 0.      
##  7 gray   0.71  0.      
##  8 Green  0.582 0.      
##  9 Blue  -0.383 2.26e- 8
## 10 GLI   -0.462 3.93e-12
## 11 BGI   -0.617 0.      
## 12 VARI  -0.88  0.      
## 13 NGRDI -0.946 0.

Spread df

all_data_spread = all_data_sbr %>% 
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean)   

all_data_spread
## # A tibble: 203 x 15
##    file    sev   BGI    BI  Blue   GLI  gray Green     HI     HUE   NGRDI   Red
##    <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>   <dbl>   <dbl> <dbl>
##  1 Ferr~ 39.7  0.400  87.8  41.1 0.196  96.2 104.  0.663  -0.263   0.0320 101. 
##  2 Ferr~ 18.6  0.379  84.7  39.7 0.231  94.0 105.  0.565  -0.953   0.0711  92.9
##  3 Ferr~ 26.4  0.503  90.3  53.1 0.165  98.7 107.  0.746  -0.668   0.0372 100. 
##  4 Ferr~  2.33 0.554  81.2  55.1 0.186  89.3  99.7 0.204  -1.50    0.101   82.0
##  5 Ferr~ 84.7  0.434 113.   51.8 0.116 121.  123.  1.62    1.23   -0.0713 142. 
##  6 Ferr~  4.08 0.505  89.3  55.5 0.196  98.7 110.  0.319  -1.43    0.0876  93.0
##  7 Ferr~  1.1  0.580  80.8  57.5 0.182  88.6  99.0 0.0999 -1.54    0.108   80.0
##  8 Ferr~ 48.5  0.506 107.   60.3 0.133 116.  122.  1.19    0.0521 -0.0118 125. 
##  9 Ferr~  2.62 0.574  82.6  57.4 0.173  90.6 100.  0.127  -1.49    0.0900  84.1
## 10 Ferr~  6.92 0.426 112.   57.7 0.199 124.  136.  0.678  -1.31    0.0465 124. 
## # ... with 193 more rows, and 3 more variables: SCI <dbl>, SI <dbl>, VARI <dbl>

GBM

train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.75*length(all_data_spread$sev),1))
# length(train)
gbm.fit = gbm(sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI,
             data = all_data_spread[train,],
             distribution = "gaussian",
              n.trees = 1000,
             interaction.depth = 3,
             shrinkage = 0.1,
             cv.folds = 5,
             n.cores = NULL, # will use all cores by default
             verbose = FALSE)
print(gbm.fit)
## gbm(formula = sev ~ BGI + BI + GLI + HI + HUE + NGRDI + VARI + 
##     gray + Red + Green + Blue + SI + SCI, distribution = "gaussian", 
##     data = all_data_spread[train, ], n.trees = 1000, interaction.depth = 3, 
##     shrinkage = 0.1, cv.folds = 5, verbose = FALSE, n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 1000 iterations were performed.
## The best cross-validation iteration was 942.
## There were 13 predictors of which 13 had non-zero influence.
sqrt(min(gbm.fit$cv.error))
## [1] 4.02846
gbm.perf(gbm.fit, method = "cv")

## [1] 942
# find index for n trees with minimum CV error
min_MSE <- which.min(gbm.fit$cv.error)
sqrt(gbm.fit$cv.error[min_MSE])
## [1] 4.02846
# best.iter <- gbm.perf(model1, method = "test")
# print(best.iter)

pred = predict(gbm.fit, newdata = all_data_spread[-train,-1], ntrees = 5000 )
## Using 942 trees...
sqrt(mean(((pred)-all_data_spread$sev[-train])^2))
## [1] 3.398297
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.9897837
plot((pred), (pred)-all_data_spread$sev[-train])
abline(a=0,b=0)

Testing various hyperparameters

Create hyperparameter grid

hyper_grid <- expand.grid(
  shrinkage = c(.001, .01, .1, .3),
  interaction.depth = c(1, 3, 5, 6),
  n.minobsinnode = c(5, 10, 15),
  bag.fraction = c(.5,.65, .8, 1), 
  optimal_trees = 0,               # a place to dump results
  min_RMSE = 0,
  CCC =0 # a place to dump results
)
# total number of combinations
nrow(hyper_grid)
## [1] 192
# randomize data
set.seed(123)
train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.8*length(all_data_spread$sev),1))

# grid search 
for(i in 1:nrow(hyper_grid)) {

# reproducibility
set.seed(123)


 # train model
gbm.tune <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray +Red+Green+Blue + SI + SCI, #<<<<<
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = hyper_grid$interaction.depth[i],
  shrinkage = hyper_grid$shrinkage[i],
  n.minobsinnode = hyper_grid$n.minobsinnode[i],
  bag.fraction = hyper_grid$bag.fraction[i],
  train.fraction = .75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE)

pred = predict(gbm.tune, newdata = all_data_spread[-train,-1], ntrees = 5000 )
 # add min training error and trees to grid
  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$valid.error))
  hyper_grid$CCC[i] = CCC(pred, all_data_spread$sev[-train])$rho.c$est#<<<<<
  
}
## Using 5000 trees...
## Using 2636 trees...
## Using 228 trees...
## Using 57 trees...
## Using 4999 trees...
## Using 1734 trees...
## Using 178 trees...
## Using 357 trees...
## Using 5000 trees...
## Using 1797 trees...
## Using 153 trees...
## Using 126 trees...
## Using 5000 trees...
## Using 1797 trees...
## Using 153 trees...
## Using 76 trees...
## Using 5000 trees...
## Using 4969 trees...
## Using 591 trees...
## Using 297 trees...
## Using 5000 trees...
## Using 4916 trees...
## Using 485 trees...
## Using 70 trees...
## Using 5000 trees...
## Using 4896 trees...
## Using 657 trees...
## Using 118 trees...
## Using 5000 trees...
## Using 4896 trees...
## Using 657 trees...
## Using 118 trees...
## Using 5000 trees...
## Using 3278 trees...
## Using 394 trees...
## Using 68 trees...
## Using 5000 trees...
## Using 2055 trees...
## Using 156 trees...
## Using 63 trees...
## Using 5000 trees...
## Using 2055 trees...
## Using 156 trees...
## Using 63 trees...
## Using 5000 trees...
## Using 2055 trees...
## Using 156 trees...
## Using 63 trees...
## Using 5000 trees...
## Using 1650 trees...
## Using 131 trees...
## Using 105 trees...
## Using 4995 trees...
## Using 1904 trees...
## Using 98 trees...
## Using 27 trees...
## Using 5000 trees...
## Using 1576 trees...
## Using 132 trees...
## Using 84 trees...
## Using 5000 trees...
## Using 1579 trees...
## Using 132 trees...
## Using 10 trees...
## Using 5000 trees...
## Using 4943 trees...
## Using 576 trees...
## Using 134 trees...
## Using 5000 trees...
## Using 4988 trees...
## Using 489 trees...
## Using 212 trees...
## Using 5000 trees...
## Using 4083 trees...
## Using 298 trees...
## Using 99 trees...
## Using 5000 trees...
## Using 4129 trees...
## Using 424 trees...
## Using 214 trees...
## Using 5000 trees...
## Using 3608 trees...
## Using 439 trees...
## Using 133 trees...
## Using 5000 trees...
## Using 2813 trees...
## Using 449 trees...
## Using 63 trees...
## Using 5000 trees...
## Using 2813 trees...
## Using 449 trees...
## Using 59 trees...
## Using 5000 trees...
## Using 2813 trees...
## Using 449 trees...
## Using 59 trees...
## Using 5000 trees...
## Using 1601 trees...
## Using 125 trees...
## Using 53 trees...
## Using 5000 trees...
## Using 1148 trees...
## Using 78 trees...
## Using 15 trees...
## Using 5000 trees...
## Using 896 trees...
## Using 80 trees...
## Using 23 trees...
## Using 5000 trees...
## Using 1161 trees...
## Using 105 trees...
## Using 17 trees...
## Using 5000 trees...
## Using 4708 trees...
## Using 728 trees...
## Using 428 trees...
## Using 5000 trees...
## Using 4236 trees...
## Using 374 trees...
## Using 118 trees...
## Using 5000 trees...
## Using 3092 trees...
## Using 301 trees...
## Using 102 trees...
## Using 5000 trees...
## Using 3103 trees...
## Using 263 trees...
## Using 109 trees...
## Using 5000 trees...
## Using 4714 trees...
## Using 655 trees...
## Using 247 trees...
## Using 5000 trees...
## Using 4756 trees...
## Using 499 trees...
## Using 127 trees...
## Using 5000 trees...
## Using 3402 trees...
## Using 292 trees...
## Using 130 trees...
## Using 5000 trees...
## Using 3402 trees...
## Using 292 trees...
## Using 130 trees...
## Using 5000 trees...
## Using 3297 trees...
## Using 355 trees...
## Using 1401 trees...
## Using 5000 trees...
## Using 4600 trees...
## Using 612 trees...
## Using 20 trees...
## Using 4999 trees...
## Using 1109 trees...
## Using 93 trees...
## Using 33 trees...
## Using 5000 trees...
## Using 565 trees...
## Using 97 trees...
## Using 27 trees...
## Using 5000 trees...
## Using 4994 trees...
## Using 1345 trees...
## Using 297 trees...
## Using 5000 trees...
## Using 2565 trees...
## Using 271 trees...
## Using 133 trees...
## Using 5000 trees...
## Using 2912 trees...
## Using 235 trees...
## Using 77 trees...
## Using 5000 trees...
## Using 3010 trees...
## Using 246 trees...
## Using 104 trees...
## Using 5000 trees...
## Using 4997 trees...
## Using 738 trees...
## Using 227 trees...
## Using 5000 trees...
## Using 4998 trees...
## Using 585 trees...
## Using 109 trees...
## Using 4999 trees...
## Using 4259 trees...
## Using 385 trees...
## Using 149 trees...
## Using 5000 trees...
## Using 3530 trees...
## Using 400 trees...
## Using 202 trees...
best_par = hyper_grid %>% 
  dplyr::arrange(-CCC) %>%
  head(10)
best_par
##    shrinkage interaction.depth n.minobsinnode bag.fraction optimal_trees
## 1      0.010                 3              5         0.80          1148
## 2      0.010                 5              5         1.00          1109
## 3      0.100                 6              5         1.00            97
## 4      0.100                 5              5         1.00            93
## 5      0.010                 3              5         1.00          4600
## 6      0.010                 1              5         0.80          1601
## 7      0.010                 1              5         0.65          1650
## 8      0.001                 3              5         0.65          4995
## 9      0.010                 6              5         0.80          1161
## 10     0.001                 3              5         0.80          5000
##    min_RMSE       CCC
## 1  2.270680 0.9958594
## 2  2.002059 0.9956714
## 3  1.975201 0.9955144
## 4  2.055946 0.9955131
## 5  2.157053 0.9955040
## 6  2.266556 0.9954981
## 7  2.375012 0.9954573
## 8  2.488595 0.9954234
## 9  2.073971 0.9953818
## 10 2.302626 0.9953742
# gbm.tune$fit

Best model

# for reproducibility
set.seed(123)

# train GBM model
gbm.fit.final <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+Red+Green+Blue+gray+SI+SCI,
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = best_par$optimal_trees[1],
  interaction.depth = best_par$interaction.depth[1],
  shrinkage = best_par$shrinkage[1],
  n.minobsinnode = best_par$n.minobsinnode[1],
  bag.fraction = best_par$bag.fraction[1], 
  train.fraction =0.75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE
  )

Relative influence

par(mar = c(5, 8, 1, 1))
summary_gbm_sbr = summary(
  gbm.fit.final, 
  cBars = 15,
  method = relative.influence, # also can use permutation.test.gbm
  las = 2
  )

rel_sbr = summary_gbm_sbr %>% 
  rownames_to_column("index") %>% 
  ggplot(aes(rel.inf, reorder(var, rel.inf)))+
  geom_col(aes(fill =rel.inf>1, color =rel.inf>1 ), width = 0.85)+
  theme_minimal_vgrid()+
  labs(x = "Relative influence (%)",
       y = "Model predictors",
       fill = "RI > 1%",
       color = "RI > 1%")
rel_sbr

# ggsave("figs/var_influence.png",dpi = 600, height = 4, width = 6)

Partial dependence plots

gbm.fit.final %>%
  pdp::partial(pred.var = "HUE", n.trees = gbm.fit.final$n.trees, grid.resolution = 100) %>%
  ggplot(aes( HUE,(yhat)))+
  geom_line()

LIME

library(lime)
model_type.gbm <- function(x, ...) {
  return("regression")
}

predict_model.gbm <- function(x, newdata, ...) {
  pred <- predict(x, newdata, n.trees = x$n.trees)
  return(as.data.frame(pred))
}
# get a few observations to perform local interpretation on
local_obs <- (all_data_spread[-train,])[1:4, ]

# apply LIME
explainer <- lime(all_data_spread[train,], gbm.fit.final)
explanation <- lime::explain(local_obs, explainer, n_features = 7, n.trees =1)
plot_features(explanation)

Prediction

# predict values for test data
pred <- predict(gbm.fit.final,
                n.trees = gbm.fit.final$n.trees,
                all_data_spread[-train,])

# results
caret::RMSE((pred), all_data_spread[-train,]$sev)
## [1] 1.926231
CCC(pred, all_data_spread$sev[-train])$rho.c$est
## [1] 0.9958621
cor(pred, all_data_spread$sev[-train])^2
## [1] 0.9921386
accuracy_sbr =data.frame(predi=pred, actual = all_data_spread$sev[-train]) %>% 
  summarise(RMSE = caret::RMSE(pred, actual),
            r = cor(pred, actual),
            s.shift = CCC(pred, actual)$s.shift,
            l.shift = CCC(pred, actual)$l.shift,
            C.b = CCC(pred, actual)$C.b,
            CCC = CCC(pred, actual)$rho.c$est,
            CIS = paste(
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[2],2),","," ",
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[3],2),sep = ""
  ))
accuracy_sbr
##       RMSE         r   s.shift     l.shift       C.b       CCC     CIS
## 1 1.926231 0.9960615 0.9916907 -0.01819114 0.9997998 0.9958621 0.99, 1

plot

conc_sbr = data.frame(predict = pred, actual =all_data_spread$sev[-train]) %>% 
ggplot(aes(actual, predict ))+
  geom_point(size =2, color = "gray")+
  geom_abline(intercept = 0, slope= 1, size = .81, color = "black", linetype = "dashed")+
  geom_smooth(method = "lm", 
              color = "red",
              size =.81, se =F,
              fullrange=T)+
  theme_minimal_grid()+
  labs(x = "Predicted Severity (%)",
       y = "Actual Severity (%)")+
  coord_equal(xlim = c(0,100),
              ylim = c(0,100))+
  xlim(0,100)


ggsave("figs/concordance.png", dpi = 600, height = 3.5, width = 4)
## `geom_smooth()` using formula 'y ~ x'

Xylella

pics<-list.files("./pics/01-Xylella-tobacco-bg-white")
# length(pics)
#indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")


box = data.frame()

for(i in 1:length(pics)){

EX.L1<-stack(paste("./pics/01-Xylella-tobacco-bg-white/",pics[i],sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)

EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=200, cropAbove=T, plot = F)

cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)


df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  mutate(gray = 0.299*Red+0.587*Green+0.114*Blue) %>% 
  gather(c(1:(3+length(index)),15), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  dplyr::summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[i])


box = box %>% 
  bind_rows(dff)}
length(unique(box$leaf))
write.table(box,"data/indexes_Xylella.txt")
box = read.table("data/indexes_Xylella.txt")
data_xy_load = read_csv("data_pics/01-Xylella-tobacco-severity.csv") %>% 
  mutate(file = as.character(File)) %>% 
  dplyr::select(-File)
## 
## -- Column specification --------------------------------------------------------
## cols(
##   File = col_double(),
##   ImageJ = col_double(),
##   LeafDoctor = col_double(),
##   APSAssess = col_double()
## )
data_xy = box %>% 
  separate(leaf, into=c("file","format"), sep =".jpg") %>% 
  dplyr::select(-format) %>% 
  full_join(data_xy_load, by="file") %>% 
  mutate(sev=ImageJ)
data_xy
##      index          mean          std           Q25           Q50           Q75
## 1      BGI  5.436164e-01  0.060121706  5.121507e-01  5.339519e-01  5.541888e-01
## 2       BI  1.671294e+02 13.092581029  1.590453e+02  1.673032e+02  1.744013e+02
## 3     Blue  1.055687e+02 17.594940645  9.485714e+01  1.037959e+02  1.121020e+02
## 4      GLI  1.386614e-01  0.020247634  1.340011e-01  1.426077e-01  1.493713e-01
## 5     gray  1.815699e+02 13.150761073  1.733458e+02  1.820882e+02  1.895008e+02
## 6    Green  1.933107e+02 13.420773604  1.847347e+02  1.940408e+02  2.020408e+02
## 7       HI  8.683842e-01  0.102006173  8.046512e-01  8.494624e-01  9.244940e-01
## 8      HUE -1.231244e+00  0.938461283 -1.564719e+00 -1.562570e+00 -1.553532e+00
## 9    NGRDI  1.513704e-02  0.011610581  8.698471e-03  1.786423e-02  2.269336e-02
## 10     Red  1.874974e+02 12.336910350  1.802041e+02  1.880408e+02  1.948163e+02
## 11     SCI -1.513704e-02  0.011610581 -2.269336e-02 -1.786423e-02 -8.698471e-03
## 12      SI  2.835890e-01  0.047290707  2.687086e-01  2.891532e-01  3.124621e-01
## 13    VARI  2.097451e-02  0.016012463  1.176282e-02  2.450909e-02  3.152252e-02
## 14     BGI  5.232702e-01  0.064259254  4.901864e-01  5.117849e-01  5.343837e-01
## 15      BI  1.617949e+02 13.149662642  1.538317e+02  1.616828e+02  1.685547e+02
## 16    Blue  9.936791e+01 18.019025309  8.900000e+01  9.702041e+01  1.052194e+02
## 17     GLI  1.489379e-01  0.022855570  1.426525e-01  1.522061e-01  1.609541e-01
## 18    gray  1.763900e+02 13.065001780  1.685468e+02  1.765641e+02  1.836820e+02
## 19   Green  1.888874e+02 13.024434760  1.812449e+02  1.894694e+02  1.965714e+02
## 20      HI  8.288865e-01  0.108060562  7.430341e-01  8.064516e-01  8.758588e-01
## 21     HUE -1.305940e+00  0.838101317 -1.565441e+00 -1.564433e+00 -1.559984e+00
## 22   NGRDI  2.076509e-02  0.013190269  1.435438e-02  2.346119e-02  2.917836e-02
## 23     Red  1.812212e+02 12.792847953  1.736122e+02  1.815612e+02  1.886735e+02
## 24     SCI -2.076509e-02  0.013190269 -2.917836e-02 -2.346119e-02 -1.435438e-02
## 25      SI  2.962883e-01  0.050157294  2.822797e-01  3.044717e-01  3.244522e-01
## 26    VARI  2.834054e-02  0.017835753  1.980149e-02  3.213349e-02  3.987774e-02
## 27     BGI  4.770135e-01  0.082275350  4.382802e-01  4.640944e-01  4.856903e-01
## 28      BI  1.346668e+02 16.903593814  1.247420e+02  1.328121e+02  1.413769e+02
## 29    Blue  7.849852e+01 21.629501426  6.740816e+01  7.530612e+01  8.242857e+01
## 30     GLI  1.841680e-01  0.032885559  1.770874e-01  1.896025e-01  2.013689e-01
## 31    gray  1.483695e+02 16.606670990  1.383943e+02  1.469750e+02  1.557476e+02
## 32   Green  1.625577e+02 15.721708271  1.530357e+02  1.617551e+02  1.703112e+02
## 33      HI  6.317971e-01  0.081442239  5.531797e-01  6.365651e-01  6.761815e-01
## 34     HUE -1.566068e+00  0.002466480 -1.567126e+00 -1.566629e+00 -1.565890e+00
## 35   NGRDI  5.079765e-02  0.014373767  4.323811e-02  5.162627e-02  6.232151e-02
## 36     Red  1.471550e+02 17.493227737  1.365714e+02  1.449184e+02  1.555765e+02
## 37     SCI -5.079765e-02  0.014373767 -6.232151e-02 -5.162627e-02 -4.323811e-02
## 38      SI  3.130982e-01  0.060454942  3.008149e-01  3.208377e-01  3.440621e-01
## 39    VARI  6.729878e-02  0.018001981  5.792041e-02  6.774116e-02  8.341990e-02
## 40     BGI  5.471168e-01  0.064567155  5.118101e-01  5.328164e-01  5.587819e-01
## 41      BI  1.626126e+02 13.429799977  1.551476e+02  1.613388e+02  1.691920e+02
## 42    Blue  1.033741e+02 18.416521184  9.302041e+01  9.967347e+01  1.090000e+02
## 43     GLI  1.380349e-01  0.023116581  1.296631e-01  1.415430e-01  1.522815e-01
## 44    gray  1.765774e+02 13.240406905  1.692520e+02  1.757616e+02  1.836343e+02
## 45   Green  1.879669e+02 13.149076689  1.804898e+02  1.875714e+02  1.952449e+02
## 46      HI  8.632352e-01  0.120741343  7.977528e-01  8.528022e-01  9.247863e-01
## 47     HUE -1.178044e+00  1.005955360 -1.564537e+00 -1.561666e+00 -1.552260e+00
## 48   NGRDI  1.582729e-02  0.014003198  8.299927e-03  1.680000e-02  2.467409e-02
## 49     Red  1.821276e+02 13.014208369  1.748571e+02  1.815306e+02  1.895306e+02
## 50     SCI -1.582729e-02  0.014003198 -2.467409e-02 -1.680000e-02 -8.299927e-03
## 51      SI  2.803030e-01  0.049074718  2.674682e-01  2.903750e-01  3.087919e-01
## 52    VARI  2.191157e-02  0.019195066  1.158766e-02  2.317333e-02  3.360512e-02
## 53     BGI  6.397902e-01  0.057576557  6.033778e-01  6.395914e-01  6.702550e-01
## 54      BI  1.883111e+02 15.966699694  1.786307e+02  1.888041e+02  1.989763e+02
## 55    Blue  1.349047e+02 19.447790916  1.220816e+02  1.347551e+02  1.473673e+02
## 56     GLI  9.997205e-02  0.022113827  8.811560e-02  9.980354e-02  1.142050e-01
## 57    gray  2.013672e+02 16.127278310  1.921515e+02  2.021308e+02  2.119078e+02
## 58   Green  2.101206e+02 16.487520281  2.018980e+02  2.112551e+02  2.204898e+02
## 59      HI  9.952901e-01  0.203793834  9.097048e-01  9.727264e-01  1.007014e+00
## 60     HUE -6.338601e-01  1.346936550 -1.555699e+00 -1.520522e+00  1.359702e+00
## 61   NGRDI  1.230542e-03  0.016915886 -5.605370e-04  2.476373e-03  8.748221e-03
## 62     Red  2.095227e+02 15.755228570  1.998367e+02  2.101735e+02  2.200612e+02
## 63     SCI -1.230542e-03  0.016915886 -8.748221e-03 -2.476373e-03  5.605370e-04
## 64      SI  2.199965e-01  0.041622674  1.968736e-01  2.194891e-01  2.451591e-01
## 65    VARI  1.781766e-03  0.024176415 -8.544055e-04  3.614236e-03  1.267687e-02
## 66     BGI  5.820188e-01  0.067428110  5.315358e-01  5.693426e-01  6.175964e-01
## 67      BI  1.772043e+02 16.401507923  1.661700e+02  1.758584e+02  1.867000e+02
## 68    Blue  1.183991e+02 20.538575261  1.033878e+02  1.151020e+02  1.297755e+02
## 69     GLI  1.248815e-01  0.029034530  1.071104e-01  1.293797e-01  1.484303e-01
## 70    gray  1.914034e+02 16.216391501  1.811177e+02  1.903582e+02  2.006643e+02
## 71   Green  2.024200e+02 15.776128292  1.937755e+02  2.017143e+02  2.111020e+02
## 72      HI  8.999821e-01  0.206456865  7.832061e-01  8.690452e-01  9.447821e-01
## 73     HUE -1.121452e+00  1.066487327 -1.565103e+00 -1.561004e+00 -1.546838e+00
## 74   NGRDI  1.236663e-02  0.019391600  5.042075e-03  1.395027e-02  2.521696e-02
## 75     Red  1.976099e+02 17.276915595  1.853112e+02  1.964898e+02  2.083673e+02
## 76     SCI -1.236663e-02  0.019391600 -2.521696e-02 -1.395027e-02 -5.042075e-03
## 77      SI  2.550979e-01  0.045179189  2.323478e-01  2.627929e-01  2.850668e-01
## 78    VARI  1.709632e-02  0.027170859  7.449380e-03  1.972998e-02  3.474857e-02
## 79     BGI  5.085819e-01  0.065712411  4.773217e-01  4.939795e-01  5.140404e-01
## 80      BI  1.445236e+02 12.891753106  1.374060e+02  1.428794e+02  1.488367e+02
## 81    Blue  8.702637e+01 17.652175236  7.822449e+01  8.355102e+01  8.957143e+01
## 82     GLI  1.571989e-01  0.024133703  1.494502e-01  1.607931e-01  1.712432e-01
## 83    gray  1.579929e+02 12.709072914  1.507976e+02  1.566197e+02  1.630469e+02
## 84   Green  1.700325e+02 12.655048196  1.627347e+02  1.690612e+02  1.759796e+02
## 85      HI  7.936470e-01  0.101355477  7.169132e-01  7.893328e-01  8.598902e-01
## 86     HUE -1.466058e+00  0.523798340 -1.565577e+00 -1.563556e+00 -1.559642e+00
## 87   NGRDI  2.601853e-02  0.013494652  1.692368e-02  2.608425e-02  3.531347e-02
## 88     Red  1.614142e+02 12.201318919  1.543061e+02  1.604082e+02  1.664898e+02
## 89     SCI -2.601853e-02  0.013494652 -3.531347e-02 -2.608425e-02 -1.692368e-02
## 90      SI  3.046540e-01  0.050377029  2.973605e-01  3.144625e-01  3.302657e-01
## 91    VARI  3.514187e-02  0.017979049  2.316398e-02  3.531491e-02  4.770609e-02
## 92     BGI  5.140943e-01  0.066878803  4.825597e-01  5.055288e-01  5.262627e-01
## 93      BI  1.206068e+02 15.753601285  1.125480e+02  1.169682e+02  1.243959e+02
## 94    Blue  7.661937e+01 17.705114033  6.989796e+01  7.322449e+01  7.700000e+01
## 95     GLI  1.916382e-01  0.028509055  1.899393e-01  1.973042e-01  2.040239e-01
## 96    gray  1.331735e+02 15.668948939  1.246965e+02  1.294918e+02  1.377841e+02
## 97   Green  1.480769e+02 14.975951780  1.396122e+02  1.446122e+02  1.533469e+02
## 98      HI  3.599747e-01  0.104268323  2.922038e-01  3.497448e-01  4.250591e-01
## 99     HUE -1.567211e+00  0.001128685 -1.567569e+00 -1.567394e+00 -1.567210e+00
## 100  NGRDI  8.445326e-02  0.017164204  7.931397e-02  8.714782e-02  9.400915e-02
## 101    Red  1.254772e+02 17.404673932  1.156122e+02  1.213878e+02  1.309796e+02
## 102    SCI -8.445326e-02  0.017164204 -9.400915e-02 -8.714782e-02 -7.931397e-02
## 103     SI  2.457563e-01  0.047373487  2.245343e-01  2.455025e-01  2.727635e-01
## 104   VARI  1.166940e-01  0.023432053  1.075013e-01  1.201967e-01  1.304114e-01
## 105    BGI  4.876649e-01  0.075177217  4.522709e-01  4.716773e-01  4.942060e-01
## 106     BI  1.293983e+02 17.900713893  1.187963e+02  1.263242e+02  1.353274e+02
## 107   Blue  7.713667e+01 21.125797394  6.622449e+01  7.298980e+01  7.975510e+01
## 108    GLI  1.826781e-01  0.030965041  1.772256e-01  1.887532e-01  1.986924e-01
## 109   gray  1.425269e+02 17.886501674  1.315521e+02  1.397158e+02  1.494310e+02
## 110  Green  1.563000e+02 17.484522103  1.453061e+02  1.538469e+02  1.641939e+02
## 111     HI  5.989870e-01  0.098148849  5.285039e-01  5.945295e-01  6.481746e-01
## 112    HUE -1.564649e+00  0.051323937 -1.567106e+00 -1.566624e+00 -1.565615e+00
## 113  NGRDI  5.457846e-02  0.016582721  4.544022e-02  5.596591e-02  6.660335e-02
## 114    Red  1.404189e+02 18.544979568  1.289592e+02  1.375306e+02  1.477143e+02
## 115    SCI -5.457846e-02  0.016582721 -6.660335e-02 -5.596591e-02 -4.544022e-02
## 116     SI  2.988513e-01  0.054816385  2.849264e-01  3.075378e-01  3.285267e-01
## 117   VARI  7.304889e-02  0.021377644  6.082658e-02  7.385281e-02  8.893299e-02
## 118    BGI  6.027203e-01  0.058716015  5.723945e-01  5.950962e-01  6.254052e-01
## 119     BI  1.761344e+02 15.816844788  1.683357e+02  1.775403e+02  1.855630e+02
## 120   Blue  1.184159e+02 18.482792674  1.081429e+02  1.177959e+02  1.268980e+02
## 121    GLI  1.017298e-01  0.028620014  8.394042e-02  1.022331e-01  1.220593e-01
## 122   gray  1.886308e+02 16.616136011  1.811637e+02  1.905397e+02  1.987039e+02
## 123  Green  1.958948e+02 18.284371202  1.886327e+02  1.984898e+02  2.073469e+02
## 124     HI  1.154198e+00  0.380323859  8.456439e-01  1.042006e+00  1.386065e+00
## 125    HUE  1.217992e-01  1.545815863 -1.560599e+00  1.536585e+00  1.567414e+00
## 126  NGRDI -1.370210e-02  0.034856111 -3.748638e-02 -4.133512e-03  1.398697e-02
## 127    Red  2.011410e+02 17.022548144  1.914694e+02  2.013265e+02  2.129592e+02
## 128    SCI  1.370210e-02  0.034856111 -1.398697e-02  4.133512e-03  3.748638e-02
## 129     SI  2.620369e-01  0.053865055  2.320727e-01  2.663788e-01  2.978484e-01
## 130   VARI -1.880448e-02  0.048624172 -5.247755e-02 -6.018349e-03  2.065343e-02
## 131    BGI  4.994713e-01  0.062777757  4.713489e-01  4.884036e-01  5.093375e-01
## 132     BI  1.497264e+02 13.170979189  1.423009e+02  1.498734e+02  1.565621e+02
## 133   Blue  8.963874e+01 16.491499847  8.120408e+01  8.761224e+01  9.475510e+01
## 134    GLI  1.691493e-01  0.023713622  1.631395e-01  1.729868e-01  1.810802e-01
## 135   gray  1.643772e+02 13.225405177  1.568870e+02  1.649127e+02  1.717896e+02
## 136  Green  1.785810e+02 12.990664628  1.712857e+02  1.795918e+02  1.863265e+02
## 137     HI  6.927919e-01  0.051306931  6.653543e-01  6.816098e-01  7.152369e-01
## 138    HUE -1.564074e+00  0.078314568 -1.566842e+00 -1.566518e+00 -1.565873e+00
## 139  NGRDI  3.993923e-02  0.008205029  3.532326e-02  4.186875e-02  4.538473e-02
## 140    Red  1.649876e+02 13.655044873  1.569592e+02  1.653673e+02  1.726939e+02
## 141    SCI -3.993923e-02  0.008205029 -4.538473e-02 -4.186875e-02 -3.532326e-02
## 142     SI  3.001807e-01  0.046054075  2.914037e-01  3.078610e-01  3.217996e-01
## 143   VARI  5.372709e-02  0.010172228  4.814663e-02  5.628613e-02  6.046925e-02
## 144    BGI  5.300425e-01  0.068896236  4.929369e-01  5.145007e-01  5.439166e-01
## 145     BI  1.496112e+02 12.531708671  1.424685e+02  1.478781e+02  1.540959e+02
## 146   Blue  9.188030e+01 17.952822086  8.239796e+01  8.789796e+01  9.583673e+01
## 147    GLI  1.381701e-01  0.025542847  1.272303e-01  1.428964e-01  1.547976e-01
## 148   gray  1.624231e+02 12.000969565  1.556090e+02  1.609982e+02  1.670893e+02
## 149  Green  1.722959e+02 11.286002785  1.661429e+02  1.711633e+02  1.766531e+02
## 150     HI  9.428877e-01  0.161228816  8.285921e-01  9.312235e-01  1.035431e+00
## 151    HUE -5.398159e-01  1.437685890 -1.561503e+00 -1.548424e+00  1.529215e+00
## 152  NGRDI  7.252632e-03  0.017531369 -4.178290e-03  8.006498e-03  2.006209e-02
## 153    Red  1.699368e+02 12.869922568  1.616531e+02  1.690408e+02  1.763265e+02
## 154    SCI -7.252632e-03  0.017531369 -2.006209e-02 -8.006498e-03  4.178290e-03
## 155     SI  3.029920e-01  0.052991791  2.897487e-01  3.124898e-01  3.317522e-01
## 156   VARI  9.889932e-03  0.023942800 -5.670858e-03  1.101950e-02  2.742532e-02
## 157    BGI  5.324968e-01  0.069526844  4.994106e-01  5.258065e-01  5.492049e-01
## 158     BI  1.135192e+02 16.596245862  1.057791e+02  1.106585e+02  1.164265e+02
## 159   Blue  7.456771e+01 18.740739102  6.738776e+01  7.153061e+01  7.530612e+01
## 160    GLI  1.866963e-01  0.030547644  1.814737e-01  1.907970e-01  2.004806e-01
## 161   gray  1.250420e+02 16.398548862  1.169126e+02  1.221848e+02  1.288145e+02
## 162  Green  1.388656e+02 15.643941717  1.306531e+02  1.361020e+02  1.435306e+02
## 163     HI  3.183277e-01  0.114943230  2.360965e-01  3.166827e-01  3.961790e-01
## 164    HUE -1.566710e+00  0.001284595 -1.567272e+00 -1.566934e+00 -1.566555e+00
## 165  NGRDI  8.693394e-02  0.018954893  8.092759e-02  8.887890e-02  9.770769e-02
## 166    Red  1.171477e+02 17.962551075  1.080000e+02  1.137959e+02  1.213265e+02
## 167    SCI -8.693394e-02  0.018954893 -9.770769e-02 -8.887890e-02 -8.092759e-02
## 168     SI  2.269589e-01  0.047345603  2.035358e-01  2.266784e-01  2.530682e-01
## 169   VARI  1.218013e-01  0.025982085  1.113648e-01  1.239330e-01  1.378939e-01
## 170    BGI  5.294524e-01  0.070994961  4.970554e-01  5.183500e-01  5.404671e-01
## 171     BI  1.198689e+02 16.040382459  1.119103e+02  1.168980e+02  1.226360e+02
## 172   Blue  7.708734e+01 19.007502082  6.926531e+01  7.340816e+01  7.796939e+01
## 173    GLI  1.738413e-01  0.029554148  1.682256e-01  1.773893e-01  1.880305e-01
## 174   gray  1.316147e+02 15.801279438  1.233271e+02  1.287510e+02  1.350395e+02
## 175  Green  1.443754e+02 15.292952874  1.356735e+02  1.417551e+02  1.486939e+02
## 176     HI  4.930155e-01  0.096269059  4.240023e-01  4.971246e-01  5.559973e-01
## 177    HUE -1.565788e+00  0.002360316 -1.566816e+00 -1.566074e+00 -1.565377e+00
## 178  NGRDI  6.380929e-02  0.016101037  5.486079e-02  6.456954e-02  7.530962e-02
## 179    Red  1.273525e+02 16.644651923  1.187653e+02  1.242245e+02  1.308980e+02
## 180    SCI -6.380929e-02  0.016101037 -7.530962e-02 -6.456954e-02 -5.486079e-02
## 181     SI  2.516587e-01  0.047862102  2.351059e-01  2.563707e-01  2.767461e-01
## 182   VARI  8.832271e-02  0.021400819  7.579152e-02  8.897186e-02  1.041362e-01
## 183    BGI  5.287628e-01  0.070768924  4.966605e-01  5.195187e-01  5.404123e-01
## 184     BI  1.203881e+02 15.185179492  1.135449e+02  1.174843e+02  1.226794e+02
## 185   Blue  7.804833e+01 18.447548041  7.097959e+01  7.475510e+01  7.853061e+01
## 186    GLI  1.822087e-01  0.029944429  1.788503e-01  1.865540e-01  1.953764e-01
## 187   gray  1.325029e+02 14.782043711  1.254898e+02  1.297281e+02  1.354214e+02
## 188  Green  1.464739e+02 13.942594373  1.395510e+02  1.439184e+02  1.499796e+02
## 189     HI  3.929090e-01  0.085102284  3.366584e-01  3.842606e-01  4.423213e-01
## 190    HUE -1.566065e+00  0.045254913 -1.567268e+00 -1.567029e+00 -1.566758e+00
## 191  NGRDI  7.719080e-02  0.015561213  7.316398e-02  8.037772e-02  8.565531e-02
## 192    Red  1.258368e+02 15.997912276  1.178367e+02  1.227347e+02  1.289796e+02
## 193    SCI -7.719080e-02  0.015561213 -8.565531e-02 -8.037772e-02 -7.316398e-02
## 194     SI  2.396596e-01  0.046485414  2.221421e-01  2.419291e-01  2.637740e-01
## 195   VARI  1.073379e-01  0.020453248  1.006270e-01  1.112730e-01  1.192763e-01
## 196    BGI  5.250583e-01  0.071932587  4.942271e-01  5.141938e-01  5.346963e-01
## 197     BI  1.191959e+02 15.958961955  1.109121e+02  1.158714e+02  1.217715e+02
## 198   Blue  7.605282e+01 19.294065268  6.783673e+01  7.234694e+01  7.728571e+01
## 199    GLI  1.740674e-01  0.029238551  1.689298e-01  1.777558e-01  1.873276e-01
## 200   gray  1.308820e+02 15.589922749  1.224805e+02  1.275846e+02  1.339535e+02
## 201  Green  1.434513e+02 14.817460119  1.351224e+02  1.401224e+02  1.468980e+02
## 202     HI  5.108120e-01  0.103492693  4.391941e-01  5.165513e-01  5.820717e-01
## 203    HUE -1.565643e+00  0.002557956 -1.566518e+00 -1.565989e+00 -1.565329e+00
## 204  NGRDI  6.172331e-02  0.016111465  5.240332e-02  6.239724e-02  7.254210e-02
## 205    Red  1.271104e+02 16.608877875  1.180204e+02  1.239184e+02  1.309184e+02
## 206    SCI -6.172331e-02  0.016111465 -7.254210e-02 -6.239724e-02 -5.240332e-02
## 207     SI  2.575596e-01  0.049680653  2.412780e-01  2.635626e-01  2.833271e-01
## 208   VARI  8.516176e-02  0.021582952  7.164497e-02  8.562143e-02  1.001330e-01
## 209    BGI  5.693282e-01  0.056593919  5.373570e-01  5.590145e-01  5.809648e-01
## 210     BI  1.731334e+02 13.744272582  1.642061e+02  1.721689e+02  1.819137e+02
## 211   Blue  1.127348e+02 15.738512027  1.026531e+02  1.108571e+02  1.195102e+02
## 212    GLI  1.254280e-01  0.024619257  1.098302e-01  1.323107e-01  1.432109e-01
## 213   gray  1.871142e+02 13.543546750  1.786573e+02  1.865333e+02  1.959722e+02
## 214  Green  1.975219e+02 12.538211491  1.906939e+02  1.978163e+02  2.055102e+02
## 215     HI  9.367249e-01  0.243034728  7.793290e-01  8.354672e-01  1.043820e+00
## 216    HUE -7.191476e-01  1.382998132 -1.564824e+00 -1.562258e+00  1.539836e+00
## 217  NGRDI  7.404515e-03  0.025480404 -4.434350e-03  1.715658e-02  2.470712e-02
## 218    Red  1.950403e+02 17.959691647  1.831020e+02  1.922245e+02  2.059184e+02
## 219    SCI -7.404515e-03  0.025480404 -2.470712e-02 -1.715658e-02  4.434350e-03
## 220     SI  2.690076e-01  0.046694233  2.535684e-01  2.767424e-01  2.964936e-01
## 221   VARI  1.065781e-02  0.035268911 -6.111649e-03  2.440895e-02  3.453757e-02
## 222    BGI  5.249571e-01  0.062383919  4.972483e-01  5.128702e-01  5.325996e-01
## 223     BI  1.596943e+02 12.559718478  1.548423e+02  1.603918e+02  1.657405e+02
## 224   Blue  9.885602e+01 16.177372461  9.148980e+01  9.722449e+01  1.033878e+02
## 225    GLI  1.535078e-01  0.022791149  1.479623e-01  1.577169e-01  1.643334e-01
## 226   gray  1.744049e+02 12.635562207  1.696160e+02  1.755141e+02  1.809110e+02
## 227  Green  1.876461e+02 12.558593906  1.828163e+02  1.891735e+02  1.945102e+02
## 228     HI  7.633942e-01  0.086782133  7.026002e-01  7.546003e-01  8.001583e-01
## 229    HUE -1.502422e+00  0.425405434 -1.566482e+00 -1.565710e+00 -1.564183e+00
## 230  NGRDI  2.885060e-02  0.011169586  2.353950e-02  3.022025e-02  3.688901e-02
## 231    Red  1.772142e+02 13.124324413  1.724694e+02  1.781837e+02  1.842653e+02
## 232    SCI -2.885060e-02  0.011169586 -3.688901e-02 -3.022025e-02 -2.353950e-02
## 233     SI  2.873387e-01  0.046363354  2.775557e-01  2.957897e-01  3.104482e-01
## 234   VARI  3.941850e-02  0.014949344  3.248707e-02  4.090942e-02  5.043292e-02
## 235    BGI  5.450818e-01  0.071943333  5.070647e-01  5.309679e-01  5.598492e-01
## 236     BI  1.537413e+02 14.514226460  1.452709e+02  1.527578e+02  1.612965e+02
## 237   Blue  9.624747e+01 19.376548376  8.561224e+01  9.309184e+01  1.020816e+02
## 238    GLI  1.291434e-01  0.026067265  1.168399e-01  1.314071e-01  1.455899e-01
## 239   gray  1.663356e+02 14.218634914  1.581210e+02  1.656253e+02  1.743097e+02
## 240  Green  1.753847e+02 13.699549873  1.675102e+02  1.749388e+02  1.832041e+02
## 241     HI  9.989140e-01  0.154262450  9.007172e-01  9.970515e-01  1.107483e+00
## 242    HUE -1.918447e-02  1.533749487 -1.555708e+00 -1.059374e+00  1.556977e+00
## 243  NGRDI  6.146476e-04  0.017263368 -1.190220e-02  3.111587e-04  1.172595e-02
## 244    Red  1.752928e+02 15.070329664  1.658776e+02  1.751633e+02  1.850000e+02
## 245    SCI -6.146476e-04  0.017263368 -1.172595e-02 -3.111587e-04  1.190220e-02
## 246     SI  2.964377e-01  0.054446703  2.857464e-01  3.082798e-01  3.249796e-01
## 247   VARI  8.426975e-04  0.023651500 -1.632448e-02  4.306633e-04  1.596546e-02
## 248    BGI  5.233619e-01  0.067891340  4.894052e-01  5.096004e-01  5.332910e-01
## 249     BI  1.474502e+02 14.535469934  1.384085e+02  1.459328e+02  1.537968e+02
## 250   Blue  8.954300e+01 19.216559334  7.900000e+01  8.600000e+01  9.425000e+01
## 251    GLI  1.384899e-01  0.021684567  1.320047e-01  1.417562e-01  1.504612e-01
## 252   gray  1.601093e+02 14.665721191  1.507577e+02  1.587924e+02  1.671115e+02
## 253  Green  1.697510e+02 15.108230617  1.599592e+02  1.685306e+02  1.775510e+02
## 254     HI  9.600963e-01  0.117854449  8.875060e-01  9.615579e-01  1.041944e+00
## 255    HUE -3.763524e-01  1.476921598 -1.557815e+00 -1.530458e+00  1.532104e+00
## 256  NGRDI  4.506612e-03  0.013642025 -4.956473e-03  4.568824e-03  1.346833e-02
## 257    Red  1.680855e+02 13.224252460  1.596939e+02  1.674286e+02  1.750408e+02
## 258    SCI -4.506612e-03  0.013642025 -1.346833e-02 -4.568824e-03  4.956473e-03
## 259     SI  3.110701e-01  0.055923605  2.990188e-01  3.218473e-01  3.405766e-01
## 260   VARI  6.327836e-03  0.018573545 -6.720936e-03  6.251881e-03  1.827972e-02
## 261    BGI  5.046310e-01  0.074173138  4.675413e-01  4.885906e-01  5.146986e-01
## 262     BI  1.304131e+02 14.578500953  1.228730e+02  1.277702e+02  1.335876e+02
## 263   Blue  7.989120e+01 19.065019246  7.089796e+01  7.606122e+01  8.185714e+01
## 264    GLI  1.767202e-01  0.029184161  1.715935e-01  1.826426e-01  1.915274e-01
## 265   gray  1.434144e+02 14.204844472  1.357792e+02  1.410068e+02  1.472919e+02
## 266  Green  1.570034e+02 13.600259390  1.492755e+02  1.548980e+02  1.617347e+02
## 267     HI  5.833598e-01  0.059904895  5.446780e-01  5.815673e-01  6.262376e-01
## 268    HUE -1.566145e+00  0.001859905 -1.566971e+00 -1.566438e+00 -1.565851e+00
## 269  NGRDI  5.448390e-02  0.011367371  4.934291e-02  5.553927e-02  6.151109e-02
## 270    Red  1.409558e+02 14.516077053  1.334694e+02  1.384694e+02  1.446122e+02
## 271    SCI -5.448390e-02  0.011367371 -6.151109e-02 -5.553927e-02 -4.934291e-02
## 272     SI  2.830816e-01  0.052495161  2.686012e-01  2.924937e-01  3.122760e-01
## 273   VARI  7.379653e-02  0.014168969  6.635839e-02  7.524178e-02  8.276499e-02
## 274    BGI  5.484175e-01  0.070442358  5.122256e-01  5.371213e-01  5.601112e-01
## 275     BI  1.533915e+02 13.434078537  1.453086e+02  1.530967e+02  1.609798e+02
## 276   Blue  9.704841e+01 18.584819973  8.663776e+01  9.446939e+01  1.031224e+02
## 277    GLI  1.322866e-01  0.023462062  1.251843e-01  1.342537e-01  1.456666e-01
## 278   gray  1.661886e+02 13.226740967  1.581150e+02  1.663080e+02  1.742349e+02
## 279  Green  1.759391e+02 13.073849723  1.679439e+02  1.763061e+02  1.841429e+02
## 280     HI  9.349741e-01  0.109724640  8.743212e-01  9.328606e-01  9.960062e-01
## 281    HUE -8.118095e-01  1.290596417 -1.558512e+00 -1.547926e+00 -1.198032e+00
## 282  NGRDI  7.278826e-03  0.012102216  4.490535e-04  7.498980e-03  1.418686e-02
## 283    Red  1.734073e+02 12.994255287  1.656531e+02  1.738571e+02  1.819388e+02
## 284    SCI -7.278826e-03  0.012102216 -1.418686e-02 -7.498980e-03 -4.490535e-04
## 285     SI  2.873982e-01  0.053222932  2.765324e-01  2.968311e-01  3.157077e-01
## 286   VARI  1.009202e-02  0.016641445  6.187760e-04  1.041315e-02  1.960147e-02
## 287    BGI  5.207860e-01  0.071626850  4.865130e-01  5.107144e-01  5.329111e-01
## 288     BI  1.395525e+02 17.068653186  1.296181e+02  1.374920e+02  1.464138e+02
## 289   Blue  8.588464e+01 20.919796122  7.487245e+01  8.273469e+01  9.046939e+01
## 290    GLI  1.510602e-01  0.024898958  1.441184e-01  1.536548e-01  1.641193e-01
## 291   gray  1.521675e+02 17.227046719  1.419040e+02  1.503289e+02  1.599090e+02
## 292  Green  1.631570e+02 17.484097310  1.526888e+02  1.615204e+02  1.716531e+02
## 293     HI  8.131070e-01  0.109803057  7.391249e-01  8.103076e-01  8.779259e-01
## 294    HUE -1.437451e+00  0.585529535 -1.564366e+00 -1.561828e+00 -1.556131e+00
## 295  NGRDI  2.267746e-02  0.013105007  1.455317e-02  2.303205e-02  3.144623e-02
## 296    Red  1.558643e+02 16.289147783  1.463061e+02  1.538980e+02  1.632296e+02
## 297    SCI -2.267746e-02  0.013105007 -3.144623e-02 -2.303205e-02 -1.455317e-02
## 298     SI  2.972665e-01  0.056629525  2.825668e-01  3.029235e-01  3.255470e-01
## 299   VARI  3.093311e-02  0.017741945  1.989417e-02  3.141559e-02  4.288234e-02
## 300    BGI  5.862999e-01  0.059612981  5.543382e-01  5.791280e-01  6.022413e-01
## 301     BI  1.681839e+02 16.083602113  1.582333e+02  1.692416e+02  1.782315e+02
## 302   Blue  1.105194e+02 19.460263483  9.816327e+01  1.098163e+02  1.197857e+02
## 303    GLI  1.055336e-01  0.019042350  9.568728e-02  1.073600e-01  1.184691e-01
## 304   gray  1.804409e+02 16.688221981  1.701113e+02  1.819661e+02  1.913046e+02
## 305  Green  1.875037e+02 17.856387955  1.763776e+02  1.892041e+02  1.995510e+02
## 306     HI  1.155520e+00  0.186526044  1.016261e+00  1.171134e+00  1.281588e+00
## 307    HUE  8.590737e-01  1.280279638  1.479247e+00  1.562279e+00  1.565508e+00
## 308  NGRDI -1.585161e-02  0.018803599 -2.912053e-02 -1.746792e-02 -1.527957e-03
## 309    Red  1.932343e+02 14.976397222  1.844082e+02  1.944286e+02  2.035510e+02
## 310    SCI  1.585161e-02  0.018803599  1.527957e-03  1.746792e-02  2.912053e-02
## 311     SI  2.769417e-01  0.050696385  2.576928e-01  2.808089e-01  3.070842e-01
## 312   VARI -2.186420e-02  0.026067428 -4.019747e-02 -2.447727e-02 -2.192770e-03
## 313    BGI  5.192105e-01  0.077532642  4.832943e-01  5.051208e-01  5.279565e-01
## 314     BI  1.238033e+02 17.501235064  1.147951e+02  1.217751e+02  1.293339e+02
## 315   Blue  7.798505e+01 21.099634579  6.795408e+01  7.457143e+01  8.144898e+01
## 316    GLI  1.722109e-01  0.030406559  1.675139e-01  1.774346e-01  1.868156e-01
## 317   gray  1.358587e+02 17.297326137  1.266558e+02  1.341108e+02  1.421687e+02
## 318  Green  1.484667e+02 16.885049723  1.391020e+02  1.471429e+02  1.556990e+02
## 319     HI  5.641178e-01  0.083052966  5.081380e-01  5.643149e-01  6.267648e-01
## 320    HUE -1.565462e+00  0.002165983 -1.566662e+00 -1.565954e+00 -1.564926e+00
## 321  NGRDI  5.525277e-02  0.013887055  4.730644e-02  5.612322e-02  6.416064e-02
## 322    Red  1.331720e+02 17.650637197  1.240969e+02  1.314082e+02  1.392041e+02
## 323    SCI -5.525277e-02  0.013887055 -6.416064e-02 -5.612322e-02 -4.730644e-02
## 324     SI  2.693215e-01  0.053556320  2.545540e-01  2.765221e-01  2.984969e-01
## 325   VARI  7.563644e-02  0.018043312  6.424849e-02  7.658353e-02  8.744597e-02
## 326    BGI  5.297517e-01  0.089256861  4.888340e-01  5.099803e-01  5.341361e-01
## 327     BI  1.216734e+02 18.012412608  1.126482e+02  1.193315e+02  1.260506e+02
## 328   Blue  7.863188e+01 22.388229120  6.810204e+01  7.437755e+01  8.048469e+01
## 329    GLI  1.761516e-01  0.037100282  1.725122e-01  1.839830e-01  1.946178e-01
## 330   gray  1.335686e+02 17.555069909  1.245575e+02  1.317249e+02  1.387731e+02
## 331  Green  1.467441e+02 16.879598346  1.378980e+02  1.454898e+02  1.532041e+02
## 332     HI  4.695773e-01  0.078643417  4.138743e-01  4.563732e-01  5.141532e-01
## 333    HUE -1.563679e+00  0.075712046 -1.567170e+00 -1.566671e+00 -1.565895e+00
## 334  NGRDI  6.704229e-02  0.017179989  6.129031e-02  7.113344e-02  7.797700e-02
## 335    Red  1.286482e+02 18.256359011  1.196786e+02  1.265102e+02  1.332041e+02
## 336    SCI -6.704229e-02  0.017179989 -7.797700e-02 -7.113344e-02 -6.129031e-02
## 337     SI  2.500272e-01  0.055117424  2.396514e-01  2.602473e-01  2.776815e-01
## 338   VARI  9.240721e-02  0.021812318  8.464712e-02  9.768407e-02  1.070202e-01
## 339    BGI  5.237393e-01  0.070387743  4.916762e-01  5.131221e-01  5.342015e-01
## 340     BI  1.317087e+02 16.350242202  1.224276e+02  1.291465e+02  1.370149e+02
## 341   Blue  8.201910e+01 19.717060635  7.220408e+01  7.869388e+01  8.548980e+01
## 342    GLI  1.566632e-01  0.026455511  1.498524e-01  1.603016e-01  1.703397e-01
## 343   gray  1.438773e+02 16.275324712  1.343790e+02  1.413986e+02  1.496976e+02
## 344  Green  1.551395e+02 16.041928337  1.455102e+02  1.526122e+02  1.615102e+02
## 345     HI  7.323317e-01  0.119954555  6.488902e-01  7.256163e-01  8.124658e-01
## 346    HUE -1.509422e+00  0.385425590 -1.565185e+00 -1.563745e+00 -1.560412e+00
## 347  NGRDI  3.308341e-02  0.015572896  2.241998e-02  3.398126e-02  4.385281e-02
## 348    Red  1.453519e+02 16.578655801  1.355816e+02  1.432653e+02  1.517143e+02
## 349    SCI -3.308341e-02  0.015572896 -4.385281e-02 -3.398126e-02 -2.241998e-02
## 350     SI  2.850766e-01  0.052848437  2.707255e-01  2.926301e-01  3.129353e-01
## 351   VARI  4.523116e-02  0.021233134  3.039835e-02  4.646386e-02  5.972904e-02
## 352    BGI  5.220014e-01  0.069163883  4.854602e-01  5.079474e-01  5.379613e-01
## 353     BI  1.314475e+02 16.742216580  1.216378e+02  1.281832e+02  1.364430e+02
## 354   Blue  8.200062e+01 19.682137241  7.155612e+01  7.789796e+01  8.516327e+01
## 355    GLI  1.609071e-01  0.026412282  1.543688e-01  1.655955e-01  1.752237e-01
## 356   gray  1.437987e+02 16.683778915  1.337721e+02  1.407774e+02  1.494348e+02
## 357  Green  1.556073e+02 16.278291231  1.455969e+02  1.529592e+02  1.618571e+02
## 358     HI  6.893229e-01  0.094072275  6.356398e-01  6.773564e-01  7.316739e-01
## 359    HUE -1.530661e+00  0.314714694 -1.565630e+00 -1.564763e+00 -1.563580e+00
## 360  NGRDI  3.886822e-02  0.012793738  3.300436e-02  4.077430e-02  4.665043e-02
## 361    Red  1.441778e+02 17.289151362  1.337755e+02  1.407959e+02  1.500612e+02
## 362    SCI -3.886822e-02  0.012793738 -4.665043e-02 -4.077430e-02 -3.300436e-02
## 363     SI  2.812932e-01  0.050396682  2.641227e-01  2.898611e-01  3.107013e-01
## 364   VARI  5.307316e-02  0.017197156  4.510258e-02  5.548978e-02  6.320527e-02
## 365    BGI  5.238761e-01  0.064520931  4.887377e-01  5.123290e-01  5.402303e-01
## 366     BI  1.225945e+02 15.852749019  1.136842e+02  1.200678e+02  1.273741e+02
## 367   Blue  7.836941e+01 17.726274608  7.016327e+01  7.513265e+01  8.082143e+01
## 368    GLI  1.793160e-01  0.027298440  1.729080e-01  1.840040e-01  1.934194e-01
## 369   gray  1.348778e+02 15.820359143  1.255633e+02  1.324440e+02  1.403712e+02
## 370  Green  1.485640e+02 15.295992026  1.391020e+02  1.463265e+02  1.546735e+02
## 371     HI  4.534645e-01  0.109331974  3.731497e-01  4.491759e-01  5.323732e-01
## 372    HUE -1.566529e+00  0.001371604 -1.567189e+00 -1.566817e+00 -1.566281e+00
## 373  NGRDI  6.986914e-02  0.017007630  6.062804e-02  7.182358e-02  8.085661e-02
## 374    Red  1.295541e+02 17.225032577  1.194490e+02  1.268571e+02  1.360612e+02
## 375    SCI -6.986914e-02  0.017007630 -8.085661e-02 -7.182358e-02 -6.062804e-02
## 376     SI  2.504249e-01  0.045659934  2.293685e-01  2.541229e-01  2.796171e-01
## 377   VARI  9.673872e-02  0.023168280  8.277490e-02  9.924512e-02  1.125975e-01
## 378    BGI  5.354317e-01  0.071313996  4.986688e-01  5.225076e-01  5.487635e-01
## 379     BI  1.273232e+02 17.883226072  1.171775e+02  1.238624e+02  1.323961e+02
## 380   Blue  8.088840e+01 20.953698464  7.004082e+01  7.636735e+01  8.428571e+01
## 381    GLI  1.521554e-01  0.028233884  1.416277e-01  1.570313e-01  1.685301e-01
## 382   gray  1.388224e+02 17.808564274  1.285083e+02  1.355726e+02  1.444364e+02
## 383  Green  1.493427e+02 17.554683179  1.389184e+02  1.463061e+02  1.550816e+02
## 384     HI  7.364305e-01  0.132900042  6.589940e-01  7.132988e-01  8.114374e-01
## 385    HUE -1.382983e+00  0.708095175 -1.564830e+00 -1.563338e+00 -1.558951e+00
## 386  NGRDI  3.202228e-02  0.017438497  2.129780e-02  3.493512e-02  4.281298e-02
## 387    Red  1.402576e+02 18.095510463  1.294490e+02  1.371633e+02  1.471020e+02
## 388    SCI -3.202228e-02  0.017438497 -4.281298e-02 -3.493512e-02 -2.129780e-02
## 389     SI  2.759451e-01  0.051104317  2.621901e-01  2.830875e-01  3.049807e-01
## 390   VARI  4.400084e-02  0.023548247  2.953804e-02  4.806749e-02  5.846652e-02
## 391    BGI  4.965653e-01  0.079627745  4.576112e-01  4.790190e-01  5.062927e-01
## 392     BI  1.405538e+02 18.275841129  1.291275e+02  1.373098e+02  1.480468e+02
## 393   Blue  8.387305e+01 21.866658446  7.244898e+01  7.885714e+01  8.744898e+01
## 394    GLI  1.689130e-01  0.033347164  1.558015e-01  1.762004e-01  1.902043e-01
## 395   gray  1.540842e+02 18.102754957  1.427699e+02  1.510731e+02  1.620069e+02
## 396  Green  1.670471e+02 17.118456525  1.567092e+02  1.642449e+02  1.745918e+02
## 397     HI  7.176766e-01  0.156018401  6.036244e-01  6.936921e-01  8.038587e-01
## 398    HUE -1.386300e+00  0.715231681 -1.566762e+00 -1.565691e+00 -1.563144e+00
## 399  NGRDI  3.762537e-02  0.021819521  2.309526e-02  4.044680e-02  5.397942e-02
## 400    Red  1.554050e+02 20.171144561  1.412857e+02  1.523776e+02  1.666173e+02
## 401    SCI -3.762537e-02  0.021819521 -5.397942e-02 -4.044680e-02 -2.309526e-02
## 402     SI  3.063417e-01  0.059244516  2.909569e-01  3.187842e-01  3.387896e-01
## 403   VARI  5.033993e-02  0.028821026  3.174379e-02  5.402534e-02  7.145717e-02
## 404    BGI  5.211453e-01  0.069683216  4.899566e-01  5.078216e-01  5.281845e-01
## 405     BI  1.427829e+02 14.179526571  1.353625e+02  1.418720e+02  1.480226e+02
## 406   Blue  8.872163e+01 18.387599503  8.004082e+01  8.600000e+01  9.218367e+01
## 407    GLI  1.610264e-01  0.027185917  1.550044e-01  1.656042e-01  1.756278e-01
## 408   gray  1.562468e+02 13.884853956  1.487423e+02  1.557257e+02  1.620402e+02
## 409  Green  1.691127e+02 13.284698595  1.617092e+02  1.689490e+02  1.754082e+02
## 410     HI  6.927941e-01  0.097553236  6.341386e-01  6.812087e-01  7.398326e-01
## 411    HUE -1.533661e+00  0.302308024 -1.566560e+00 -1.565762e+00 -1.564461e+00
## 412  NGRDI  3.856387e-02  0.013762036  3.097191e-02  4.032369e-02  4.751631e-02
## 413    Red  1.567337e+02 14.609785540  1.484286e+02  1.560510e+02  1.632245e+02
## 414    SCI -3.856387e-02  0.013762036 -4.751631e-02 -4.032369e-02 -3.097191e-02
## 415     SI  2.823817e-01  0.049759910  2.722940e-01  2.911007e-01  3.073090e-01
## 416   VARI  5.256782e-02  0.018302823  4.258658e-02  5.482058e-02  6.426120e-02
## 417    BGI  5.554579e-01  0.070899774  5.164319e-01  5.414773e-01  5.696930e-01
## 418     BI  1.625161e+02 13.595106263  1.553504e+02  1.619489e+02  1.690269e+02
## 419   Blue  1.021844e+02 19.439602379  9.126531e+01  9.897959e+01  1.082653e+02
## 420    GLI  1.173093e-01  0.024944652  1.026677e-01  1.201435e-01  1.340897e-01
## 421   gray  1.750791e+02 13.771141478  1.678362e+02  1.749311e+02  1.823608e+02
## 422  Green  1.829619e+02 14.707116395  1.747143e+02  1.830612e+02  1.918163e+02
## 423     HI  1.115773e+00  0.221058421  9.355420e-01  1.069990e+00  1.256200e+00
## 424    HUE  4.073203e-01  1.486136146 -1.548492e+00  1.549868e+00  1.565141e+00
## 425  NGRDI -1.242718e-02  0.024077290 -2.765778e-02 -7.236320e-03  6.693440e-03
## 426    Red  1.873961e+02 12.679792582  1.814082e+02  1.877347e+02  1.941429e+02
## 427    SCI  1.242718e-02  0.024077290 -6.693440e-03  7.236320e-03  2.765778e-02
## 428     SI  2.993312e-01  0.060193384  2.797104e-01  3.094472e-01  3.342742e-01
## 429   VARI -1.665706e-02  0.032480951 -3.780662e-02 -1.023866e-02  9.349649e-03
## 430    BGI  5.400814e-01  0.071925536  5.025206e-01  5.282392e-01  5.562977e-01
## 431     BI  1.166009e+02 17.649485240  1.074675e+02  1.127090e+02  1.206427e+02
## 432   Blue  7.733526e+01 19.813312323  6.912245e+01  7.300000e+01  7.744898e+01
## 433    GLI  1.819086e-01  0.031842210  1.784304e-01  1.885623e-01  1.972451e-01
## 434   gray  1.281973e+02 17.401674800  1.187700e+02  1.244686e+02  1.332056e+02
## 435  Green  1.418990e+02 16.402334762  1.326735e+02  1.385306e+02  1.474490e+02
## 436     HI  3.358040e-01  0.141950025  2.295720e-01  3.342149e-01  4.326241e-01
## 437    HUE -1.566216e+00  0.034081696 -1.567239e+00 -1.566956e+00 -1.566581e+00
## 438  NGRDI  8.332864e-02  0.021703746  7.463147e-02  8.632743e-02  9.736409e-02
## 439    Red  1.206901e+02 19.444305373  1.095102e+02  1.164490e+02  1.271429e+02
## 440    SCI -8.332864e-02  0.021703746 -9.736409e-02 -8.632743e-02 -7.463147e-02
## 441     SI  2.237954e-01  0.049262601  1.963739e-01  2.257212e-01  2.552688e-01
## 442   VARI  1.172587e-01  0.030378973  1.027964e-01  1.203482e-01  1.378702e-01
## 443    BGI  5.346590e-01  0.072480016  4.939433e-01  5.217933e-01  5.500966e-01
## 444     BI  1.586044e+02 15.232760193  1.480257e+02  1.592621e+02  1.674833e+02
## 445   Blue  9.974399e+01 19.625582486  8.767347e+01  9.753061e+01  1.065306e+02
## 446    GLI  1.492086e-01  0.030265053  1.345262e-01  1.519202e-01  1.694415e-01
## 447   gray  1.728196e+02 14.910294112  1.625260e+02  1.740088e+02  1.820270e+02
## 448  Green  1.853867e+02 13.983644221  1.761429e+02  1.864490e+02  1.939796e+02
## 449     HI  7.831766e-01  0.157492115  6.635638e-01  7.496516e-01  8.944681e-01
## 450    HUE -1.195512e+00  0.992478235 -1.566905e+00 -1.565174e+00 -1.557669e+00
## 451  NGRDI  2.685379e-02  0.020567838  1.169958e-02  2.797829e-02  4.233799e-02
## 452    Red  1.760092e+02 16.887354429  1.637551e+02  1.780816e+02  1.872653e+02
## 453    SCI -2.685379e-02  0.020567838 -4.233799e-02 -2.797829e-02 -1.169958e-02
## 454     SI  2.815520e-01  0.052593393  2.700558e-01  2.900691e-01  3.096276e-01
## 455   VARI  3.671980e-02  0.027712050  1.633129e-02  3.888313e-02  5.778265e-02
## 456    BGI  5.329802e-01  0.068257145  4.972797e-01  5.179919e-01  5.447359e-01
## 457     BI  1.635488e+02 12.945816619  1.563341e+02  1.626355e+02  1.691450e+02
## 458   Blue  1.015314e+02 18.453136243  9.114286e+01  9.816327e+01  1.066735e+02
## 459    GLI  1.421414e-01  0.024387848  1.354700e-01  1.466366e-01  1.556862e-01
## 460   gray  1.778464e+02 12.679172879  1.707905e+02  1.773190e+02  1.839119e+02
## 461  Green  1.895340e+02 12.360020850  1.827551e+02  1.893469e+02  1.959796e+02
## 462     HI  8.747204e-01  0.131212043  7.900273e-01  8.588413e-01  9.270067e-01
## 463    HUE -1.168346e+00  1.016582098 -1.564745e+00 -1.561492e+00 -1.552287e+00
## 464  NGRDI  1.498786e-02  0.014486335  8.352107e-03  1.641707e-02  2.505604e-02
## 465    Red  1.839979e+02 12.930806008  1.768367e+02  1.834286e+02  1.907908e+02
## 466    SCI -1.498786e-02  0.014486335 -2.505604e-02 -1.641707e-02 -8.352107e-03
## 467     SI  2.934039e-01  0.052761594  2.782379e-01  3.035117e-01  3.241928e-01
## 468   VARI  2.054019e-02  0.019810177  1.169519e-02  2.246015e-02  3.427607e-02
## 469    BGI  4.952852e-01  0.074527453  4.633113e-01  4.770828e-01  4.955592e-01
## 470     BI  1.483821e+02 13.641513684  1.411250e+02  1.470247e+02  1.536048e+02
## 471   Blue  8.830111e+01 19.299668071  7.940816e+01  8.428571e+01  9.048469e+01
## 472    GLI  1.708486e-01  0.028348125  1.664811e-01  1.775059e-01  1.849260e-01
## 473   gray  1.629022e+02 13.177974186  1.557700e+02  1.620764e+02  1.687101e+02
## 474  Green  1.770550e+02 12.436010126  1.703316e+02  1.767755e+02  1.831429e+02
## 475     HI  6.954710e-01  0.075476999  6.471875e-01  6.810771e-01  7.264981e-01
## 476    HUE -1.554096e+00  0.184547448 -1.567000e+00 -1.566607e+00 -1.565683e+00
## 477  NGRDI  4.007713e-02  0.011720850  3.398657e-02  4.252720e-02  4.800629e-02
## 478    Red  1.635605e+02 13.610611750  1.558367e+02  1.626531e+02  1.703469e+02
## 479    SCI -4.007713e-02  0.011720850 -4.800629e-02 -4.252720e-02 -3.398657e-02
## 480     SI  3.047971e-01  0.054012704  3.008835e-01  3.168290e-01  3.300526e-01
## 481   VARI  5.365908e-02  0.014958927  4.605950e-02  5.680146e-02  6.384184e-02
## 482    BGI  5.442703e-01  0.061071971  5.108391e-01  5.316004e-01  5.582811e-01
## 483     BI  1.716234e+02 14.241336350  1.631903e+02  1.709974e+02  1.790346e+02
## 484   Blue  1.089607e+02 17.636281895  9.822449e+01  1.065102e+02  1.161020e+02
## 485    GLI  1.421834e-01  0.021910846  1.347103e-01  1.470360e-01  1.555523e-01
## 486   gray  1.866801e+02 14.352778874  1.783008e+02  1.863492e+02  1.944195e+02
## 487  Green  1.994104e+02 14.152619315  1.912653e+02  1.997143e+02  2.073878e+02
## 488     HI  8.212868e-01  0.070612097  7.768051e-01  8.064516e-01  8.744676e-01
## 489    HUE -1.538299e+00  0.264743541 -1.565584e+00 -1.564448e+00 -1.561154e+00
## 490  NGRDI  2.093508e-02  0.008721118  1.436158e-02  2.239640e-02  2.677305e-02
## 491    Red  1.913201e+02 14.850767867  1.826939e+02  1.904796e+02  1.994898e+02
## 492    SCI -2.093508e-02  0.008721118 -2.677305e-02 -2.239640e-02 -1.436158e-02
## 493     SI  2.778811e-01  0.044888872  2.657416e-01  2.845454e-01  3.020852e-01
## 494   VARI  2.884547e-02  0.011799911  1.994195e-02  3.088715e-02  3.656663e-02
## 495    BGI  5.609856e-01  0.083853109  5.083240e-01  5.498266e-01  5.932783e-01
## 496     BI  1.670620e+02 17.653470060  1.547940e+02  1.676717e+02  1.777593e+02
## 497   Blue  1.075657e+02 23.939310334  9.142857e+01  1.054082e+02  1.186122e+02
## 498    GLI  1.253213e-01  0.029575411  1.108515e-01  1.287683e-01  1.441070e-01
## 499   gray  1.804022e+02 17.343059987  1.685135e+02  1.814482e+02  1.917514e+02
## 500  Green  1.900296e+02 16.765897302  1.789388e+02  1.913469e+02  2.014286e+02
## 501     HI  9.881746e-01  0.136377215  8.972003e-01  9.842738e-01  1.071831e+00
## 502    HUE -1.310478e-01  1.526569539 -1.558046e+00 -1.485676e+00  1.551483e+00
## 503  NGRDI  2.175897e-03  0.014219689 -7.472696e-03  1.663536e-03  1.156175e-02
## 504    Red  1.892721e+02 17.445625372  1.773469e+02  1.901020e+02  2.008571e+02
## 505    SCI -2.175897e-03  0.014219689 -1.156175e-02 -1.663536e-03  7.472696e-03
## 506     SI  2.828440e-01  0.063074857  2.559740e-01  2.878431e-01  3.218741e-01
## 507   VARI  2.831771e-03  0.019719296 -1.061048e-02  2.336085e-03  1.601880e-02
## 508    BGI  4.907328e-01  0.082737798  4.463164e-01  4.736623e-01  5.029475e-01
## 509     BI  1.258034e+02 17.748456556  1.152794e+02  1.224017e+02  1.316392e+02
## 510   Blue  7.546188e+01 21.803555833  6.334694e+01  7.081633e+01  7.971429e+01
## 511    GLI  1.814295e-01  0.035422105  1.730819e-01  1.888755e-01  2.022825e-01
## 512   gray  1.384293e+02 17.366016781  1.278518e+02  1.353896e+02  1.449447e+02
## 513  Green  1.516203e+02 16.236901794  1.413265e+02  1.493469e+02  1.586735e+02
## 514     HI  6.031791e-01  0.133998693  5.242137e-01  5.767701e-01  6.542321e-01
## 515    HUE -1.513842e+00  0.393318934 -1.566849e+00 -1.566225e+00 -1.565233e+00
## 516  NGRDI  5.401157e-02  0.020239338  4.432275e-02  5.768847e-02  6.762455e-02
## 517    Red  1.365403e+02 18.948153899  1.247347e+02  1.330000e+02  1.434286e+02
## 518    SCI -5.401157e-02  0.020239338 -6.762455e-02 -5.768847e-02 -4.432275e-02
## 519     SI  2.973053e-01  0.059220510  2.826931e-01  3.059369e-01  3.296189e-01
## 520   VARI  7.225054e-02  0.026248824  5.963046e-02  7.719531e-02  8.968269e-02
## 521    BGI  5.651627e-01  0.070270315  5.274869e-01  5.538134e-01  5.826988e-01
## 522     BI  1.670819e+02 15.641189025  1.580787e+02  1.673641e+02  1.760445e+02
## 523   Blue  1.076521e+02 20.462167790  9.581633e+01  1.058367e+02  1.157143e+02
## 524    GLI  1.207909e-01  0.022726178  1.122594e-01  1.245610e-01  1.342208e-01
## 525   gray  1.802434e+02 15.751071332  1.714407e+02  1.807724e+02  1.899738e+02
## 526  Green  1.893013e+02 16.011764860  1.803878e+02  1.900204e+02  1.997755e+02
## 527     HI  1.022842e+00  0.144981807  9.306627e-01  1.003411e+00  1.127672e+00
## 528    HUE  6.781276e-02  1.515971846 -1.552779e+00  1.209506e+00  1.559581e+00
## 529  NGRDI -2.392550e-03  0.015107182 -1.358419e-02 -3.861856e-04  8.088395e-03
## 530    Red  1.901378e+02 15.217866158  1.816122e+02  1.912245e+02  1.996122e+02
## 531    SCI  2.392550e-03  0.015107182 -8.088395e-03  3.861856e-04  1.358419e-02
## 532     SI  2.823076e-01  0.055760004  2.632192e-01  2.889896e-01  3.141424e-01
## 533   VARI -3.142441e-03  0.020961349 -1.872552e-02 -5.305826e-04  1.108096e-02
## 534    BGI  5.439335e-01  0.075919415  5.029933e-01  5.276799e-01  5.597873e-01
## 535     BI  1.440937e+02 17.319382774  1.331346e+02  1.421219e+02  1.508383e+02
## 536   Blue  9.128441e+01 22.083875611  7.859184e+01  8.683673e+01  9.681633e+01
## 537    GLI  1.369913e-01  0.024998268  1.291644e-01  1.409693e-01  1.518008e-01
## 538   gray  1.562958e+02 17.194593334  1.453090e+02  1.546045e+02  1.635488e+02
## 539  Green  1.660256e+02 17.041478112  1.550612e+02  1.645306e+02  1.734898e+02
## 540     HI  8.913054e-01  0.108882529  8.199500e-01  8.882682e-01  9.541194e-01
## 541    HUE -1.120553e+00  1.048817281 -1.561080e+00 -1.555048e+00 -1.532264e+00
## 542  NGRDI  1.233694e-02  0.011861531  5.203341e-03  1.300793e-02  2.096676e-02
## 543    Red  1.619811e+02 16.601483266  1.513265e+02  1.609592e+02  1.696735e+02
## 544    SCI -1.233694e-02  0.011861531 -2.096676e-02 -1.300793e-02 -5.203341e-03
## 545     SI  2.869752e-01  0.058659716  2.703882e-01  2.991266e-01  3.199344e-01
## 546   VARI  1.708056e-02  0.016435109  7.163965e-03  1.779963e-02  2.903145e-02
## 547    BGI  5.159173e-01  0.063766630  4.829690e-01  5.044009e-01  5.278829e-01
## 548     BI  1.576645e+02 13.721336042  1.495583e+02  1.582037e+02  1.651035e+02
## 549   Blue  9.650251e+01 17.179029550  8.663265e+01  9.479592e+01  1.023673e+02
## 550    GLI  1.588122e-01  0.023509295  1.527699e-01  1.627243e-01  1.710447e-01
## 551   gray  1.724887e+02 13.820421603  1.643430e+02  1.733682e+02  1.805926e+02
## 552  Green  1.861704e+02 13.624547658  1.781429e+02  1.873673e+02  1.948367e+02
## 553     HI  7.408370e-01  0.050689452  7.052632e-01  7.397849e-01  7.737494e-01
## 554    HUE -1.564936e+00  0.036986414 -1.566522e+00 -1.565863e+00 -1.565061e+00
## 555  NGRDI  3.237852e-02  0.007694591  2.758137e-02  3.252652e-02  3.811958e-02
## 556    Red  1.745999e+02 14.179625477  1.664898e+02  1.757143e+02  1.826327e+02
## 557    SCI -3.237852e-02  0.007694591 -3.811958e-02 -3.252652e-02 -2.758137e-02
## 558     SI  2.922959e-01  0.047084031  2.800412e-01  2.996543e-01  3.180760e-01
## 559   VARI  4.392920e-02  0.009710020  3.760518e-02  4.396396e-02  5.151563e-02
## 560    BGI  5.666081e-01  0.066185437  5.313483e-01  5.560075e-01  5.815648e-01
## 561     BI  1.672388e+02 15.254461292  1.578224e+02  1.671204e+02  1.766321e+02
## 562   Blue  1.078770e+02 19.747760866  9.587755e+01  1.055918e+02  1.165510e+02
## 563    GLI  1.197491e-01  0.022304631  1.106805e-01  1.219795e-01  1.330704e-01
## 564   gray  1.803647e+02 15.424924103  1.707613e+02  1.805379e+02  1.904228e+02
## 565  Green  1.893122e+02 15.887831016  1.791429e+02  1.895816e+02  2.003673e+02
## 566     HI  1.030893e+00  0.167196006  9.074960e-01  1.016514e+00  1.163739e+00
## 567    HUE  8.921013e-02  1.530465766 -1.556655e+00  1.472025e+00  1.562077e+00
## 568  NGRDI -3.208784e-03  0.017743870 -1.747636e-02 -1.633745e-03  1.018313e-02
## 569    Red  1.904362e+02 14.821982349  1.813061e+02  1.910204e+02  2.002449e+02
## 570    SCI  3.208784e-03  0.017743870 -1.018313e-02  1.633745e-03  1.747636e-02
## 571     SI  2.815712e-01  0.053005356  2.629915e-01  2.887514e-01  3.138900e-01
## 572   VARI -4.231938e-03  0.024516247 -2.408287e-02 -2.268541e-03  1.417627e-02
## 573    BGI  5.055943e-01  0.073446911  4.700520e-01  4.922193e-01  5.176691e-01
## 574     BI  1.281643e+02 18.853688053  1.168745e+02  1.254604e+02  1.346853e+02
## 575   Blue  7.861401e+01 21.139395268  6.780102e+01  7.522449e+01  8.159184e+01
## 576    GLI  1.740048e-01  0.030266609  1.668375e-01  1.782952e-01  1.895035e-01
## 577   gray  1.407645e+02 18.996462889  1.290265e+02  1.382042e+02  1.481471e+02
## 578  Green  1.536511e+02 18.707555429  1.417959e+02  1.510612e+02  1.619949e+02
## 579     HI  6.128575e-01  0.103030323  5.365854e-01  6.287918e-01  6.766391e-01
## 580    HUE -1.565167e+00  0.003559577 -1.566714e+00 -1.566028e+00 -1.564698e+00
## 581  NGRDI  5.071917e-02  0.016691568  4.042076e-02  4.989788e-02  6.258580e-02
## 582    Red  1.391616e+02 19.824444129  1.269439e+02  1.366020e+02  1.471990e+02
## 583    SCI -5.071917e-02  0.016691568 -6.258580e-02 -4.989788e-02 -4.042076e-02
## 584     SI  2.856032e-01  0.052925437  2.693275e-01  2.942268e-01  3.141070e-01
## 585   VARI  6.865797e-02  0.021810797  5.478477e-02  6.691776e-02  8.472075e-02
## 586    BGI  5.695572e-01  0.063098581  5.349127e-01  5.587229e-01  5.829474e-01
## 587     BI  1.717000e+02 13.650988803  1.640337e+02  1.711276e+02  1.786286e+02
## 588   Blue  1.124495e+02 18.462811866  1.020408e+02  1.097755e+02  1.186327e+02
## 589    GLI  1.277223e-01  0.022444609  1.191524e-01  1.299448e-01  1.420012e-01
## 590   gray  1.857400e+02 13.433976159  1.782143e+02  1.855378e+02  1.930289e+02
## 591  Green  1.965788e+02 13.214038616  1.892653e+02  1.969796e+02  2.040000e+02
## 592     HI  9.041533e-01  0.101551396  8.174045e-01  8.848758e-01  9.536239e-01
## 593    HUE -1.041056e+00  1.127944155 -1.563560e+00 -1.559081e+00 -1.540524e+00
## 594  NGRDI  1.080787e-02  0.011320207  4.620462e-03  1.198167e-02  1.990020e-02
## 595    Red  1.924048e+02 13.362369902  1.847041e+02  1.923673e+02  2.003265e+02
## 596    SCI -1.080787e-02  0.011320207 -1.990020e-02 -1.198167e-02 -4.620462e-03
## 597     SI  2.662022e-01  0.045228656  2.551637e-01  2.741124e-01  2.908000e-01
## 598   VARI  1.505163e-02  0.015658227  6.570312e-03  1.693834e-02  2.800701e-02
## 599    BGI  5.136999e-01  0.067818433  4.833272e-01  5.003712e-01  5.217761e-01
## 600     BI  1.198540e+02 15.102103461  1.123906e+02  1.172470e+02  1.230915e+02
## 601   Blue  7.425426e+01 18.716515505  6.595918e+01  7.106122e+01  7.637755e+01
## 602    GLI  1.685783e-01  0.030022294  1.558108e-01  1.732643e-01  1.882053e-01
## 603   gray  1.314305e+02 14.821883632  1.239274e+02  1.291451e+02  1.352574e+02
## 604  Green  1.430537e+02 14.567105097  1.352653e+02  1.414286e+02  1.478163e+02
## 605     HI  6.382261e-01  0.176387068  4.856875e-01  6.291667e-01  7.384014e-01
## 606    HUE -1.461387e+00  0.531711148 -1.566605e+00 -1.564688e+00 -1.561563e+00
## 607  NGRDI  4.680895e-02  0.024643389  3.050796e-02  4.601382e-02  6.880573e-02
## 608    Red  1.304114e+02 15.213986066  1.219286e+02  1.274082e+02  1.345918e+02
## 609    SCI -4.680895e-02  0.024643389 -6.880573e-02 -4.601382e-02 -3.050796e-02
## 610     SI  2.811871e-01  0.050980546  2.636429e-01  2.847900e-01  3.105250e-01
## 611   VARI  6.386241e-02  0.033348409  4.215504e-02  6.274008e-02  9.372058e-02
## 612    BGI  5.233699e-01  0.071366342  4.852351e-01  5.082110e-01  5.365184e-01
## 613     BI  1.540889e+02 17.517171455  1.424442e+02  1.531945e+02  1.640565e+02
## 614   Blue  9.335171e+01 21.686472899  8.009184e+01  8.948980e+01  1.016122e+02
## 615    GLI  1.357483e-01  0.025168397  1.239059e-01  1.393655e-01  1.524221e-01
## 616   gray  1.671046e+02 18.089294852  1.549565e+02  1.665128e+02  1.779650e+02
## 617  Green  1.767388e+02 19.283769323  1.636531e+02  1.761224e+02  1.888571e+02
## 618     HI  9.959410e-01  0.203502594  8.178332e-01  9.719725e-01  1.165941e+00
## 619    HUE -1.038766e-01  1.543646333 -1.563215e+00 -1.517131e+00  1.561744e+00
## 620  NGRDI  4.205196e-04  0.024052663 -1.981832e-02  3.196535e-03  2.071091e-02
## 621    Red  1.763105e+02 16.493211830  1.652245e+02  1.762245e+02  1.869388e+02
## 622    SCI -4.205196e-04  0.024052663 -2.071091e-02 -3.196535e-03  1.981832e-02
## 623     SI  3.148103e-01  0.062226054  2.904577e-01  3.268891e-01  3.535252e-01
## 624   VARI  1.060480e-03  0.032360432 -2.630472e-02  4.421577e-03  2.886495e-02
## 625    BGI  5.090994e-01  0.074640085  4.719389e-01  4.961193e-01  5.220881e-01
## 626     BI  1.261842e+02 19.187278450  1.141480e+02  1.223852e+02  1.319595e+02
## 627   Blue  7.658158e+01 22.064905577  6.455102e+01  7.152041e+01  7.990306e+01
## 628    GLI  1.579552e-01  0.029446425  1.450048e-01  1.615677e-01  1.764518e-01
## 629   gray  1.378492e+02 19.436966167  1.252792e+02  1.343742e+02  1.445752e+02
## 630  Green  1.483860e+02 19.731447740  1.351633e+02  1.453571e+02  1.560051e+02
## 631     HI  7.845365e-01  0.159833062  6.716482e-01  7.406094e-01  8.911468e-01
## 632    HUE -1.161258e+00  1.021305644 -1.565094e+00 -1.562742e+00 -1.550539e+00
## 633  NGRDI  2.734472e-02  0.021018167  1.268927e-02  3.069510e-02  4.376964e-02
## 634    Red  1.405229e+02 19.127103160  1.281837e+02  1.366531e+02  1.476939e+02
## 635    SCI -2.734472e-02  0.021018167 -4.376964e-02 -3.069510e-02 -1.268927e-02
## 636     SI  3.036723e-01  0.058445554  2.857008e-01  3.136611e-01  3.372737e-01
## 637   VARI  3.699704e-02  0.028058685  1.751993e-02  4.203108e-02  5.874688e-02
## 638    BGI  6.078474e-01  0.053070687  5.768072e-01  5.972071e-01  6.251866e-01
## 639     BI  1.867474e+02 13.368470137  1.806434e+02  1.866594e+02  1.943435e+02
## 640   Blue  1.286178e+02 16.006173385  1.193878e+02  1.264694e+02  1.362449e+02
## 641    GLI  1.133765e-01  0.018648996  1.052220e-01  1.163055e-01  1.247095e-01
## 642   gray  2.009108e+02 13.510402642  1.951436e+02  2.013281e+02  2.087615e+02
## 643  Green  2.112135e+02 13.470802690  2.058980e+02  2.122245e+02  2.191633e+02
## 644     HI  9.306279e-01  0.094401483  8.666211e-01  9.325843e-01  9.744526e-01
## 645    HUE -9.545181e-01  1.190772573 -1.561704e+00 -1.553566e+00 -1.518738e+00
## 646  NGRDI  7.204478e-03  0.009141375  2.319307e-03  7.101086e-03  1.381579e-02
## 647    Red  2.082477e+02 14.195514712  2.020408e+02  2.085918e+02  2.166327e+02
## 648    SCI -7.204478e-03  0.009141375 -1.381579e-02 -7.101086e-03 -2.319307e-03
## 649     SI  2.384427e-01  0.036727602  2.269988e-01  2.445077e-01  2.597786e-01
## 650   VARI  1.027617e-02  0.013126463  3.409407e-03  1.006711e-02  1.984564e-02
## 651    BGI  4.952912e-01  0.083176449  4.551537e-01  4.763584e-01  4.980520e-01
## 652     BI  1.370597e+02 16.845397255  1.276754e+02  1.353550e+02  1.432755e+02
## 653   Blue  8.254839e+01 21.922877265  7.188265e+01  7.875510e+01  8.534694e+01
## 654    GLI  1.783104e-01  0.032992951  1.746986e-01  1.845826e-01  1.950874e-01
## 655   gray  1.507312e+02 16.440247545  1.413634e+02  1.494971e+02  1.576889e+02
## 656  Green  1.648639e+02 15.608272220  1.557755e+02  1.642653e+02  1.721786e+02
## 657     HI  6.140678e-01  0.064753533  5.465704e-01  6.327898e-01  6.645768e-01
## 658    HUE -1.566132e+00  0.010084477 -1.567193e+00 -1.566778e+00 -1.566183e+00
## 659  NGRDI  5.154886e-02  0.013234603  4.475784e-02  5.044159e-02  6.250312e-02
## 660    Red  1.489818e+02 17.125448397  1.387959e+02  1.476327e+02  1.567755e+02
## 661    SCI -5.154886e-02  0.013234603 -6.250312e-02 -5.044159e-02 -4.475784e-02
## 662     SI  2.952387e-01  0.057882639  2.873269e-01  3.077318e-01  3.252201e-01
## 663   VARI  6.910328e-02  0.016349416  5.998907e-02  6.696758e-02  8.424664e-02
## 664    BGI  5.336188e-01  0.069163995  4.974636e-01  5.207194e-01  5.435871e-01
## 665     BI  1.628448e+02 14.040329393  1.551261e+02  1.632000e+02  1.703755e+02
## 666   Blue  1.019810e+02 19.183728951  9.108163e+01  9.983673e+01  1.084082e+02
## 667    GLI  1.473044e-01  0.022631135  1.439975e-01  1.510857e-01  1.584462e-01
## 668   gray  1.774100e+02 14.015288664  1.696882e+02  1.782003e+02  1.856003e+02
## 669  Green  1.900616e+02 14.075069732  1.823061e+02  1.911429e+02  1.987959e+02
## 670     HI  7.994245e-01  0.068526871  7.397882e-01  8.057697e-01  8.494624e-01
## 671    HUE -1.548913e+00  0.198724403 -1.565273e+00 -1.564533e+00 -1.562722e+00
## 672  NGRDI  2.346648e-02  0.007541160  1.899536e-02  2.353198e-02  2.749106e-02
## 673    Red  1.813310e+02 13.270621244  1.743878e+02  1.821837e+02  1.890816e+02
## 674    SCI -2.346648e-02  0.007541160 -2.749106e-02 -2.353198e-02 -1.899536e-02
## 675     SI  2.851300e-01  0.052935122  2.714772e-01  2.935806e-01  3.165445e-01
## 676   VARI  3.228889e-02  0.010389648  2.570829e-02  3.227931e-02  3.721519e-02
## 677    BGI  5.363549e-01  0.066370741  4.990220e-01  5.208711e-01  5.507217e-01
## 678     BI  1.622543e+02 13.517443985  1.535825e+02  1.610629e+02  1.692846e+02
## 679   Blue  1.016159e+02 17.771590643  9.083673e+01  9.851020e+01  1.077755e+02
## 680    GLI  1.441727e-01  0.026540456  1.330787e-01  1.498287e-01  1.615670e-01
## 681   gray  1.765660e+02 13.151570506  1.683397e+02  1.758571e+02  1.838684e+02
## 682  Green  1.886103e+02 12.235751556  1.814082e+02  1.885510e+02  1.957347e+02
## 683     HI  8.399318e-01  0.128388623  7.240705e-01  8.250756e-01  9.142663e-01
## 684    HUE -1.225113e+00  0.941316253 -1.565847e+00 -1.563267e+00 -1.555597e+00
## 685  NGRDI  1.982248e-02  0.015405983  9.541884e-03  2.033617e-02  3.306392e-02
## 686    Red  1.814967e+02 14.877843221  1.715918e+02  1.800000e+02  1.905918e+02
## 687    SCI -1.982248e-02  0.015405983 -3.306392e-02 -2.033617e-02 -9.541884e-03
## 688     SI  2.860697e-01  0.046315678  2.752465e-01  2.956003e-01  3.116864e-01
## 689   VARI  2.697639e-02  0.020994841  1.335392e-02  2.796167e-02  4.544025e-02
## 690    BGI  6.234243e-01  0.051347026  5.922737e-01  6.224598e-01  6.486731e-01
## 691     BI  1.843406e+02 12.407116365  1.776757e+02  1.858557e+02  1.925398e+02
## 692   Blue  1.293257e+02 16.050989182  1.193776e+02  1.301837e+02  1.389592e+02
## 693    GLI  1.058335e-01  0.016277606  9.732254e-02  1.061799e-01  1.163689e-01
## 694   gray  1.976974e+02 12.384748219  1.912227e+02  1.993255e+02  2.059830e+02
## 695  Green  2.068853e+02 12.362877362  2.006224e+02  2.085510e+02  2.151020e+02
## 696     HI  9.713776e-01  0.070392318  9.328708e-01  9.742944e-01  1.000000e+00
## 697    HUE -6.490884e-01  1.295622142 -1.550777e+00 -1.517756e+00  0.000000e+00
## 698  NGRDI  2.770496e-03  0.006281432  0.000000e+00  2.355203e-03  6.779014e-03
## 699    Red  2.057279e+02 12.046072879  1.995306e+02  2.077347e+02  2.138776e+02
## 700    SCI -2.770496e-03  0.006281432 -6.779014e-03 -2.355203e-03  0.000000e+00
## 701     SI  2.305398e-01  0.037646495  2.102963e-01  2.289809e-01  2.537458e-01
## 702   VARI  4.026234e-03  0.009183291  0.000000e+00  3.453866e-03  9.674783e-03
## 703    BGI  5.906602e-01  0.061360229  5.524775e-01  5.819846e-01  6.144118e-01
## 704     BI  1.843845e+02 13.148442961  1.763827e+02  1.839973e+02  1.917711e+02
## 705   Blue  1.211344e+02 17.486057261  1.104796e+02  1.186327e+02  1.285510e+02
## 706    GLI  1.017174e-01  0.018319622  9.203013e-02  1.035036e-01  1.132234e-01
## 707   gray  1.975377e+02 13.297464069  1.894378e+02  1.975564e+02  2.055002e+02
## 708  Green  2.045594e+02 13.395182083  1.964082e+02  2.049592e+02  2.127755e+02
## 709     HI  1.200024e+00  0.124504484  1.132856e+00  1.201386e+00  1.278084e+00
## 710    HUE  1.345772e+00  0.781644949  1.561811e+00  1.564769e+00  1.566465e+00
## 711  NGRDI -1.996159e-02  0.012247129 -2.809257e-02 -2.050877e-02 -1.378561e-02
## 712    Red  2.128829e+02 13.755183913  2.042653e+02  2.130612e+02  2.218980e+02
## 713    SCI  1.996159e-02  0.012247129  1.378561e-02  2.050877e-02  2.809257e-02
## 714     SI  2.775080e-01  0.049154190  2.554118e-01  2.839601e-01  3.094629e-01
## 715   VARI -2.788813e-02  0.017001666 -3.912620e-02 -2.866801e-02 -1.930492e-02
## 716    BGI  4.767877e-01  0.076903317  4.424008e-01  4.592376e-01  4.794548e-01
## 717     BI  1.392395e+02 15.366369679  1.317755e+02  1.375969e+02  1.444194e+02
## 718   Blue  8.129589e+01 20.211299872  7.193878e+01  7.738776e+01  8.410204e+01
## 719    GLI  1.872960e-01  0.030701071  1.849219e-01  1.949402e-01  2.019633e-01
## 720   gray  1.536365e+02 15.083155810  1.461844e+02  1.525704e+02  1.595581e+02
## 721  Green  1.688923e+02 14.408747167  1.617755e+02  1.686531e+02  1.754694e+02
## 722     HI  5.981487e-01  0.046545932  5.505618e-01  6.099713e-01  6.369103e-01
## 723    HUE -1.566952e+00  0.001345488 -1.567621e+00 -1.567265e+00 -1.566838e+00
## 724  NGRDI  5.572581e-02  0.011047152  5.159066e-02  5.675984e-02  6.399175e-02
## 725    Red  1.512674e+02 15.483874450  1.435153e+02  1.495510e+02  1.568367e+02
## 726    SCI -5.572581e-02  0.011047152 -6.399175e-02 -5.675984e-02 -5.159066e-02
## 727     SI  3.083466e-01  0.055223945  3.004248e-01  3.178120e-01  3.355263e-01
## 728   VARI  7.396256e-02  0.013183607  6.808397e-02  7.355888e-02  8.496368e-02
## 729    BGI  6.032492e-01  0.062880036  5.665221e-01  5.984609e-01  6.301392e-01
## 730     BI  1.736074e+02 28.457258013  1.659649e+02  1.813097e+02  1.920285e+02
## 731   Blue  1.163127e+02 26.091302186  1.051224e+02  1.199388e+02  1.320816e+02
## 732    GLI  9.616794e-02  0.045626857  8.176099e-02  1.083292e-01  1.254361e-01
## 733   gray  1.857804e+02 31.707609235  1.792353e+02  1.953846e+02  2.059950e+02
## 734  Green  1.927309e+02 36.476874261  1.885918e+02  2.056531e+02  2.150816e+02
## 735     HI  1.295403e+00  0.725287264  9.073698e-01  1.012385e+00  1.266070e+00
## 736    HUE  6.505451e-02  1.542607590 -1.557563e+00  1.464413e+00  1.565774e+00
## 737  NGRDI -2.190857e-02  0.056443762 -2.370389e-02 -1.214831e-03  9.810347e-03
## 738    Red  1.986211e+02 26.694723101  1.884388e+02  2.043878e+02  2.165204e+02
## 739    SCI  2.190857e-02  0.056443762 -9.810347e-03  1.214831e-03  2.370389e-02
## 740     SI  2.694197e-01  0.059308892  2.421634e-01  2.628703e-01  2.895090e-01
## 741   VARI -3.004305e-02  0.076733608 -3.413615e-02 -1.707213e-03  1.390930e-02
## 742    BGI  6.608370e-01  0.043804392  6.339592e-01  6.554491e-01  6.800178e-01
## 743     BI  1.919331e+02 14.236019575  1.838461e+02  1.934966e+02  2.015874e+02
## 744   Blue  1.387411e+02 15.774465958  1.295306e+02  1.390510e+02  1.479388e+02
## 745    GLI  8.166800e-02  0.017496028  7.120438e-02  8.178244e-02  9.318041e-02
## 746   gray  2.038340e+02 14.767399361  1.957254e+02  2.059767e+02  2.138687e+02
## 747  Green  2.096147e+02 15.624670969  2.016939e+02  2.123469e+02  2.200612e+02
## 748     HI  1.228318e+00  0.243940739  1.068273e+00  1.216686e+00  1.360324e+00
## 749    HUE  1.067478e+00  1.110616393  1.548512e+00  1.563919e+00  1.566450e+00
## 750  NGRDI -1.830239e-02  0.019713099 -2.792836e-02 -1.767597e-02 -5.747744e-03
## 751    Red  2.173034e+02 14.894451577  2.085918e+02  2.181939e+02  2.275102e+02
## 752    SCI  1.830239e-02  0.019713099  5.747744e-03  1.767597e-02  2.792836e-02
## 753     SI  2.223938e-01  0.035662006  2.052356e-01  2.225195e-01  2.423292e-01
## 754   VARI -2.683824e-02  0.028399977 -4.164850e-02 -2.629774e-02 -8.586295e-03
## 755    BGI  4.963050e-01  0.073444184  4.596644e-01  4.764354e-01  5.001154e-01
## 756     BI  1.418642e+02 16.635375975  1.317519e+02  1.386728e+02  1.485321e+02
## 757   Blue  8.440060e+01 20.735227775  7.381633e+01  7.900000e+01  8.697959e+01
## 758    GLI  1.672326e-01  0.029428239  1.573240e-01  1.747358e-01  1.860547e-01
## 759   gray  1.555060e+02 16.393764664  1.453570e+02  1.528568e+02  1.627708e+02
## 760  Green  1.684070e+02 15.653267092  1.587143e+02  1.665918e+02  1.755510e+02
## 761     HI  7.360677e-01  0.120886715  6.470307e-01  6.882540e-01  8.199401e-01
## 762    HUE -1.465058e+00  0.522683401 -1.566622e+00 -1.565708e+00 -1.561889e+00
## 763  NGRDI  3.500862e-02  0.017432143  2.014504e-02  4.046740e-02  4.870738e-02
## 764    Red  1.572891e+02 17.533095896  1.455918e+02  1.540816e+02  1.665714e+02
## 765    SCI -3.500862e-02  0.017432143 -4.870738e-02 -4.046740e-02 -2.014504e-02
## 766     SI  3.083513e-01  0.054457255  2.998362e-01  3.218687e-01  3.385897e-01
## 767   VARI  4.682874e-02  0.022951465  2.751032e-02  5.425122e-02  6.458670e-02
## 768    BGI  5.879011e-01  0.061850301  5.507415e-01  5.762660e-01  6.108035e-01
## 769     BI  1.806679e+02 13.499396994  1.723232e+02  1.811220e+02  1.890370e+02
## 770   Blue  1.188510e+02 18.960246330  1.075408e+02  1.168571e+02  1.272551e+02
## 771    GLI  1.050895e-01  0.018761346  9.529544e-02  1.072040e-01  1.175052e-01
## 772   gray  1.937799e+02 13.618550429  1.852717e+02  1.945903e+02  2.025116e+02
## 773  Green  2.012828e+02 14.193564088  1.925714e+02  2.021837e+02  2.107959e+02
## 774     HI  1.153393e+00  0.178428124  1.021892e+00  1.156526e+00  1.280097e+00
## 775    HUE  8.875292e-01  1.266464458  1.516593e+00  1.563088e+00  1.566288e+00
## 776  NGRDI -1.579716e-02  0.017893962 -2.875175e-02 -1.657241e-02 -2.350120e-03
## 777    Red  2.076182e+02 12.761460651  1.996122e+02  2.081020e+02  2.158673e+02
## 778    SCI  1.579716e-02  0.017893962  2.350120e-03  1.657241e-02  2.875175e-02
## 779     SI  2.757619e-01  0.053393651  2.510746e-01  2.839929e-01  3.098180e-01
## 780   VARI -2.176301e-02  0.024845566 -3.960463e-02 -2.311477e-02 -3.325079e-03
## 781    BGI  5.864472e-01  0.073778484  5.358409e-01  5.760101e-01  6.222618e-01
## 782     BI  1.466735e+02 23.025185723  1.311307e+02  1.484114e+02  1.622069e+02
## 783   Blue  9.536840e+01 24.564633438  7.951020e+01  9.353061e+01  1.083878e+02
## 784    GLI  9.622130e-02  0.060560453  4.670676e-02  1.187224e-01  1.433228e-01
## 785   gray  1.568098e+02 26.091990762  1.402566e+02  1.613986e+02  1.749981e+02
## 786  Green  1.623239e+02 32.050590891  1.453673e+02  1.716122e+02  1.845306e+02
## 787     HI  1.415924e+00  0.925803361  8.165785e-01  9.099307e-01  1.822424e+00
## 788    HUE -3.424832e-01  1.514432586 -1.562261e+00 -1.552045e+00  1.567510e+00
## 789  NGRDI -2.929527e-02  0.075356800 -6.261533e-02  8.569839e-03  2.155741e-02
## 790    Red  1.694101e+02 18.847371714  1.561633e+02  1.688980e+02  1.818776e+02
## 791    SCI  2.929527e-02  0.075356800 -2.155741e-02 -8.569839e-03  6.261533e-02
## 792     SI  2.898002e-01  0.071569873  2.532771e-01  2.851537e-01  3.245449e-01
## 793   VARI -3.936821e-02  0.101748513 -8.886065e-02  1.244002e-02  2.979241e-02
## 794    BGI  6.584637e-01  0.055567861  6.201099e-01  6.504906e-01  6.882962e-01
## 795     BI  1.939397e+02 14.736774250  1.845409e+02  1.949802e+02  2.040201e+02
## 796   Blue  1.413372e+02 18.530469036  1.286837e+02  1.406735e+02  1.527704e+02
## 797    GLI  9.000267e-02  0.018822835  7.859394e-02  9.276735e-02  1.033320e-01
## 798   gray  2.065247e+02 14.496589366  1.975772e+02  2.079326e+02  2.164403e+02
## 799  Green  2.140168e+02 14.112464723  2.056735e+02  2.156633e+02  2.235867e+02
## 800     HI  1.081668e+00  0.115270996  1.003372e+00  1.054054e+00  1.132383e+00
## 801    HUE  8.390084e-01  1.249126982  1.175641e+00  1.544383e+00  1.558319e+00
## 802  NGRDI -6.070114e-03  0.008386717 -1.011802e-02 -4.733728e-03 -2.991629e-04
## 803    Red  2.166702e+02 14.883136897  2.075102e+02  2.180204e+02  2.270765e+02
## 804    SCI  6.070114e-03  0.008386717  2.991629e-04  4.733728e-03  1.011802e-02
## 805     SI  2.130881e-01  0.036944184  1.927199e-01  2.170519e-01  2.374317e-01
## 806   VARI -9.181675e-03  0.012675286 -1.533073e-02 -6.981754e-03 -4.310898e-04
## 807    BGI  5.252285e-01  0.072450206  4.897937e-01  5.116636e-01  5.336676e-01
## 808     BI  1.619602e+02 14.686173970  1.536855e+02  1.618490e+02  1.685587e+02
## 809   Blue  1.000442e+02 20.495266847  8.895918e+01  9.730612e+01  1.049592e+02
## 810    GLI  1.492687e-01  0.025058667  1.444776e-01  1.528915e-01  1.616725e-01
## 811   gray  1.765262e+02 14.432636832  1.682649e+02  1.767711e+02  1.838126e+02
## 812  Green  1.891114e+02 14.083649253  1.807551e+02  1.896735e+02  1.967959e+02
## 813     HI  8.177332e-01  0.080804091  7.378599e-01  8.166704e-01  8.777977e-01
## 814    HUE -1.534086e+00  0.273919485 -1.565714e+00 -1.563684e+00 -1.560046e+00
## 815  NGRDI  2.208385e-02  0.010173725  1.420980e-02  2.185759e-02  3.021689e-02
## 816    Red  1.809793e+02 14.019428440  1.733673e+02  1.815102e+02  1.885102e+02
## 817    SCI -2.208385e-02  0.010173725 -3.021689e-02 -2.185759e-02 -1.420980e-02
## 818     SI  2.940206e-01  0.055638997  2.807332e-01  3.035689e-01  3.251066e-01
## 819   VARI  3.010799e-02  0.013759882  1.942462e-02  2.997483e-02  4.163301e-02
## 820    BGI  6.644490e-01  0.058889432  6.194996e-01  6.552901e-01  7.117511e-01
## 821     BI  1.924538e+02 17.435830759  1.802988e+02  1.918905e+02  2.068018e+02
## 822   Blue  1.413701e+02 21.864834438  1.250408e+02  1.384898e+02  1.598163e+02
## 823    GLI  8.727709e-02  0.018279757  7.260718e-02  8.959835e-02  1.015088e-01
## 824   gray  2.046374e+02 17.179843445  1.928910e+02  2.046483e+02  2.186620e+02
## 825  Green  2.116941e+02 16.922437595  2.002857e+02  2.122857e+02  2.251224e+02
## 826     HI  1.096857e+00  0.103782669  1.025075e+00  1.094980e+00  1.174312e+00
## 827    HUE  1.009635e+00  1.155492078  1.518767e+00  1.554558e+00  1.561193e+00
## 828  NGRDI -7.626938e-03  0.008270597 -1.268319e-02 -8.263614e-03 -2.434299e-03
## 829    Red  2.149054e+02 16.695046967  2.037347e+02  2.147347e+02  2.284286e+02
## 830    SCI  7.626938e-03  0.008270597  2.434299e-03  8.263614e-03  1.268319e-02
## 831     SI  2.103683e-01  0.042225532  1.761900e-01  2.139093e-01  2.414926e-01
## 832   VARI -1.138427e-02  0.012260612 -1.959698e-02 -1.211563e-02 -3.526702e-03
## 833    BGI  5.027097e-01  0.067334059  4.714096e-01  4.927040e-01  5.119752e-01
## 834     BI  1.505484e+02 13.970945293  1.425070e+02  1.513280e+02  1.585097e+02
## 835   Blue  8.919961e+01 18.557558081  7.937245e+01  8.804082e+01  9.519898e+01
## 836    GLI  1.540684e-01  0.025207854  1.450773e-01  1.583017e-01  1.685665e-01
## 837   gray  1.643874e+02 14.214106207  1.560261e+02  1.657379e+02  1.732905e+02
## 838  Green  1.762330e+02 14.988840699  1.673316e+02  1.781020e+02  1.866327e+02
## 839     HI  8.591382e-01  0.146497602  7.342044e-01  8.253012e-01  9.521445e-01
## 840    HUE -9.404625e-01  1.226693297 -1.565763e+00 -1.563230e+00 -1.539686e+00
## 841  NGRDI  1.815431e-02  0.018876351  5.397814e-03  2.246767e-02  3.335130e-02
## 842    Red  1.697989e+02 12.833991451  1.623265e+02  1.709898e+02  1.773827e+02
## 843    SCI -1.815431e-02  0.018876351 -3.335130e-02 -2.246767e-02 -5.397814e-03
## 844     SI  3.170402e-01  0.054824593  3.002515e-01  3.211826e-01  3.471662e-01
## 845   VARI  2.447713e-02  0.025187399  7.542159e-03  3.000085e-02  4.493357e-02
## 846    BGI  5.401996e-01  0.060484950  5.093409e-01  5.291851e-01  5.499103e-01
## 847     BI  1.717271e+02 13.543024645  1.639424e+02  1.711667e+02  1.783935e+02
## 848   Blue  1.086757e+02 18.247335771  9.857143e+01  1.062041e+02  1.140000e+02
## 849    GLI  1.453791e-01  0.021072499  1.404852e-01  1.495929e-01  1.568516e-01
## 850   gray  1.869982e+02 13.364030048  1.792988e+02  1.869496e+02  1.941124e+02
## 851  Green  2.002204e+02 13.033207500  1.927959e+02  2.007755e+02  2.075918e+02
## 852     HI  7.962183e-01  0.065145621  7.199483e-01  8.064516e-01  8.494624e-01
## 853    HUE -1.562826e+00  0.051495215 -1.566236e+00 -1.564793e+00 -1.563266e+00
## 854  NGRDI  2.395892e-02  0.008153070  1.838009e-02  2.299750e-02  3.020949e-02
## 855    Red  1.909022e+02 13.258302149  1.833878e+02  1.904898e+02  1.981633e+02
## 856    SCI -2.395892e-02  0.008153070 -3.020949e-02 -2.299750e-02 -1.838009e-02
## 857     SI  2.785010e-01  0.045531620  2.668452e-01  2.842253e-01  3.037266e-01
## 858   VARI  3.303924e-02  0.011078534  2.513405e-02  3.173461e-02  4.225260e-02
## 859    BGI  5.095070e-01  0.080433409  4.679955e-01  4.899000e-01  5.165715e-01
## 860     BI  1.407327e+02 17.775659232  1.297490e+02  1.366746e+02  1.480760e+02
## 861   Blue  8.506327e+01 22.686944448  7.267857e+01  7.934694e+01  8.964286e+01
## 862    GLI  1.555301e-01  0.028867897  1.491384e-01  1.611795e-01  1.713214e-01
## 863   gray  1.536071e+02 17.583689370  1.424809e+02  1.496647e+02  1.618749e+02
## 864  Green  1.649445e+02 17.174186065  1.539592e+02  1.609592e+02  1.739847e+02
## 865     HI  8.145347e-01  0.119336862  7.205048e-01  8.114187e-01  8.917800e-01
## 866    HUE -1.350941e+00  0.761779914 -1.564849e+00 -1.562290e+00 -1.555784e+00
## 867  NGRDI  2.355922e-02  0.015079984  1.317728e-02  2.407351e-02  3.497375e-02
## 868    Red  1.574831e+02 17.663902522  1.458827e+02  1.546531e+02  1.663418e+02
## 869    SCI -2.355922e-02  0.015079984 -3.497375e-02 -2.407351e-02 -1.317728e-02
## 870     SI  3.072162e-01  0.061912014  2.924830e-01  3.218014e-01  3.437263e-01
## 871   VARI  3.176585e-02  0.020371423  1.780102e-02  3.240083e-02  4.737910e-02
## 872    BGI  6.381156e-01  0.056982616  6.025020e-01  6.348491e-01  6.659326e-01
## 873     BI  1.812765e+02 15.467716855  1.719753e+02  1.828488e+02  1.913189e+02
## 874   Blue  1.293654e+02 19.008309869  1.173673e+02  1.295306e+02  1.402041e+02
## 875    GLI  9.896265e-02  0.020212190  8.684980e-02  9.868596e-02  1.104740e-01
## 876   gray  1.937770e+02 15.291710174  1.846557e+02  1.957343e+02  2.038467e+02
## 877  Green  2.018648e+02 14.938236710  1.931020e+02  2.040000e+02  2.116531e+02
## 878     HI  1.022236e+00  0.118894477  9.538188e-01  1.042996e+00  1.108108e+00
## 879    HUE  3.096260e-01  1.494619069 -1.538058e+00  1.534416e+00  1.555965e+00
## 880  NGRDI -1.339624e-03  0.010780131 -9.105692e-03 -3.662333e-03  4.397402e-03
## 881    Red  2.024572e+02 15.590105378  1.932041e+02  2.047143e+02  2.129388e+02
## 882    SCI  1.339624e-03  0.010780131 -4.397402e-03  3.662333e-03  9.105692e-03
## 883     SI  2.236804e-01  0.039405350  2.036586e-01  2.251856e-01  2.474863e-01
## 884   VARI -2.104214e-03  0.015698941 -1.357954e-02 -5.446467e-03  6.428597e-03
## 885    BGI  5.210521e-01  0.080448550  4.780648e-01  4.984161e-01  5.299018e-01
## 886     BI  1.271799e+02 17.810726833  1.167866e+02  1.235113e+02  1.327078e+02
## 887   Blue  7.827965e+01 21.283298058  6.738776e+01  7.326531e+01  8.123469e+01
## 888    GLI  1.522480e-01  0.041884703  1.490965e-01  1.648938e-01  1.749898e-01
## 889   gray  1.385866e+02 17.576059017  1.280797e+02  1.353327e+02  1.442482e+02
## 890  Green  1.486326e+02 17.443377170  1.383776e+02  1.460204e+02  1.548571e+02
## 891     HI  8.416389e-01  0.455435999  6.749029e-01  7.158597e-01  8.195212e-01
## 892    HUE -1.261554e+00  0.914286777 -1.564590e+00 -1.563423e+00 -1.559197e+00
## 893  NGRDI  2.440967e-02  0.038159032  2.167239e-02  3.658354e-02  4.264516e-02
## 894    Red  1.418575e+02 19.384455288  1.293878e+02  1.372449e+02  1.493367e+02
## 895    SCI -2.440967e-02  0.038159032 -4.264516e-02 -3.658354e-02 -2.167239e-02
## 896     SI  2.963610e-01  0.056637459  2.840955e-01  3.080511e-01  3.255671e-01
## 897   VARI  3.288493e-02  0.052562000  2.941903e-02  4.950771e-02  5.754157e-02
## 898    BGI  5.453743e-01  0.060725423  5.159841e-01  5.383914e-01  5.587139e-01
## 899     BI  1.679055e+02 13.738553642  1.602777e+02  1.689485e+02  1.757478e+02
## 900   Blue  1.062119e+02 17.615024466  9.651020e+01  1.055918e+02  1.134286e+02
## 901    GLI  1.371677e-01  0.021175504  1.299605e-01  1.394883e-01  1.484421e-01
## 902   gray  1.823077e+02 13.864531741  1.746202e+02  1.836658e+02  1.907016e+02
## 903  Green  1.938567e+02 13.973839530  1.860204e+02  1.955306e+02  2.027347e+02
## 904     HI  8.823504e-01  0.106801179  8.050383e-01  8.797092e-01  9.551044e-01
## 905    HUE -1.131290e+00  1.037107801 -1.564435e+00 -1.560164e+00 -1.542158e+00
## 906  NGRDI  1.362842e-02  0.012242606  4.942275e-03  1.379203e-02  2.276527e-02
## 907    Red  1.886478e+02 13.716253402  1.812449e+02  1.902041e+02  1.968980e+02
## 908    SCI -1.362842e-02  0.012242606 -2.276527e-02 -1.379203e-02 -4.942275e-03
## 909     SI  2.835643e-01  0.047315931  2.690711e-01  2.876748e-01  3.082603e-01
## 910   VARI  1.885334e-02  0.016919476  6.899720e-03  1.909397e-02  3.162754e-02
## 911    BGI  6.098708e-01  0.048515839  5.858978e-01  6.034535e-01  6.211456e-01
## 912     BI  1.823296e+02 13.962473545  1.751734e+02  1.834618e+02  1.906842e+02
## 913   Blue  1.242767e+02 16.088114131  1.157551e+02  1.240204e+02  1.318163e+02
## 914    GLI  1.024320e-01  0.017583817  9.683495e-02  1.056287e-01  1.127174e-01
## 915   gray  1.953989e+02 14.446472862  1.882687e+02  1.969838e+02  2.042943e+02
## 916  Green  2.032988e+02 15.191455491  1.962551e+02  2.053265e+02  2.127347e+02
## 917     HI  1.101349e+00  0.190407192  9.750000e-01  1.074074e+00  1.185532e+00
## 918    HUE  6.642535e-01  1.388298867 -1.515729e+00  1.552404e+00  1.563644e+00
## 919  NGRDI -9.330426e-03  0.016570835 -1.789507e-02 -7.035849e-03  2.367722e-03
## 920    Red  2.070067e+02 14.162906822  1.997143e+02  2.080204e+02  2.154898e+02
## 921    SCI  9.330426e-03  0.016570835 -2.367722e-03  7.035849e-03  1.789507e-02
## 922     SI  2.520741e-01  0.038316149  2.395319e-01  2.539443e-01  2.715795e-01
## 923   VARI -1.319924e-02  0.023501379 -2.553830e-02 -1.015334e-02  3.458256e-03
## 924    BGI  5.775280e-01  0.059268366  5.466155e-01  5.684733e-01  5.917077e-01
## 925     BI  1.798084e+02 13.804685710  1.713951e+02  1.805878e+02  1.888358e+02
## 926   Blue  1.160994e+02 17.545167739  1.059337e+02  1.151633e+02  1.240612e+02
## 927    GLI  1.065681e-01  0.019658257  9.628659e-02  1.085298e-01  1.187541e-01
## 928   gray  1.929994e+02 13.980393668  1.846489e+02  1.939929e+02  2.024705e+02
## 929  Green  2.003368e+02 14.118793944  1.922194e+02  2.014286e+02  2.099694e+02
## 930     HI  1.181091e+00  0.170105717  1.070511e+00  1.180301e+00  1.300244e+00
## 931    HUE  1.074290e+00  1.115935823  1.550280e+00  1.563870e+00  1.566862e+00
## 932  NGRDI -1.855927e-02  0.016684623 -3.099037e-02 -1.903932e-02 -6.918338e-03
## 933    Red  2.079141e+02 14.682147471  1.988520e+02  2.091633e+02  2.182857e+02
## 934    SCI  1.855927e-02  0.016684623  6.918338e-03  1.903932e-02  3.099037e-02
## 935     SI  2.864660e-01  0.048097403  2.748939e-01  2.934670e-01  3.118238e-01
## 936   VARI -2.565464e-02  0.023132179 -4.302774e-02 -2.624358e-02 -9.655805e-03
## 937    BGI  4.988361e-01  0.074401554  4.642952e-01  4.861383e-01  5.067953e-01
## 938     BI  1.355695e+02 17.247869426  1.263497e+02  1.341900e+02  1.412329e+02
## 939   Blue  8.162961e+01 21.147861264  7.140816e+01  7.851020e+01  8.481633e+01
## 940    GLI  1.712671e-01  0.030139937  1.637478e-01  1.754849e-01  1.874303e-01
## 941   gray  1.487775e+02 16.999392020  1.394489e+02  1.476704e+02  1.551090e+02
## 942  Green  1.617816e+02 16.236082165  1.527551e+02  1.609184e+02  1.682041e+02
## 943     HI  6.774191e-01  0.121874296  5.974020e-01  6.708747e-01  7.426549e-01
## 944    HUE -1.520831e+00  0.359287687 -1.566691e+00 -1.565826e+00 -1.564166e+00
## 945  NGRDI  4.270895e-02  0.018104473  3.172117e-02  4.405891e-02  5.501470e-02
## 946    Red  1.488492e+02 18.058860357  1.383520e+02  1.476327e+02  1.566327e+02
## 947    SCI -4.270895e-02  0.018104473 -5.501470e-02 -4.405891e-02 -3.172117e-02
## 948     SI  2.991275e-01  0.055117447  2.839054e-01  3.075274e-01  3.302507e-01
## 949   VARI  5.741578e-02  0.023915457  4.302970e-02  5.902586e-02  7.356978e-02
## 950    BGI  6.452998e-01  0.045936947  6.177228e-01  6.405857e-01  6.623352e-01
## 951     BI  1.866355e+02 12.561795684  1.787373e+02  1.879469e+02  1.951089e+02
## 952   Blue  1.335245e+02 14.971982518  1.240816e+02  1.336327e+02  1.418571e+02
## 953    GLI  9.298681e-02  0.014564540  8.694741e-02  9.459459e-02  1.019445e-01
## 954   gray  1.991362e+02 12.779960596  1.912188e+02  2.006840e+02  2.079671e+02
## 955  Green  2.065551e+02 13.098926523  1.984490e+02  2.081633e+02  2.155510e+02
## 956     HI  1.087286e+00  0.096963535  1.027787e+00  1.075134e+00  1.124432e+00
## 957    HUE  1.057341e+00  1.096607559  1.520282e+00  1.551048e+00  1.557895e+00
## 958  NGRDI -7.409015e-03  0.007937124 -1.060440e-02 -6.675982e-03 -2.554079e-03
## 959    Red  2.095872e+02 12.471785917  2.018367e+02  2.112653e+02  2.181735e+02
## 960    SCI  7.409015e-03  0.007937124  2.554079e-03  6.675982e-03  1.060440e-02
## 961     SI  2.235270e-01  0.032708226  2.100503e-01  2.258321e-01  2.434022e-01
## 962   VARI -1.088981e-02  0.011693814 -1.542738e-02 -9.900166e-03 -3.674180e-03
## 963    BGI  4.926107e-01  0.076055516  4.584638e-01  4.762635e-01  4.967913e-01
## 964     BI  1.449054e+02 15.102726740  1.368226e+02  1.435785e+02  1.503030e+02
## 965   Blue  8.557046e+01 20.320668320  7.593878e+01  8.185714e+01  8.810204e+01
## 966    GLI  1.684179e-01  0.029608806  1.596530e-01  1.722198e-01  1.855755e-01
## 967   gray  1.589155e+02 14.771443191  1.510003e+02  1.579749e+02  1.649268e+02
## 968  Green  1.722092e+02 14.180157965  1.646735e+02  1.718163e+02  1.787347e+02
## 969     HI  7.372966e-01  0.110425505  6.428760e-01  7.145973e-01  8.276914e-01
## 970    HUE -1.543911e+00  0.236156202 -1.566825e+00 -1.565429e+00 -1.562419e+00
## 971  NGRDI  3.483607e-02  0.016167620  2.112037e-02  3.589904e-02  4.866875e-02
## 972    Red  1.607814e+02 15.298838110  1.517092e+02  1.598367e+02  1.680663e+02
## 973    SCI -3.483607e-02  0.016167620 -4.866875e-02 -3.589904e-02 -2.112037e-02
## 974     SI  3.121250e-01  0.057069655  3.029319e-01  3.241564e-01  3.414389e-01
## 975   VARI  4.650008e-02  0.021178488  2.848770e-02  4.808487e-02  6.453123e-02
## 976    BGI  5.500808e-01  0.059219728  5.190774e-01  5.385491e-01  5.614153e-01
## 977     BI  1.698625e+02 13.085738901  1.620775e+02  1.697667e+02  1.766736e+02
## 978   Blue  1.077964e+02 17.529332955  9.781633e+01  1.056429e+02  1.135510e+02
## 979    GLI  1.325800e-01  0.020327091  1.250778e-01  1.367276e-01  1.448008e-01
## 980   gray  1.841312e+02 12.984661127  1.763847e+02  1.844599e+02  1.912380e+02
## 981  Green  1.950923e+02 12.850621842  1.874898e+02  1.959184e+02  2.024031e+02
## 982     HI  9.238338e-01  0.096337608  8.541667e-01  9.227202e-01  9.837735e-01
## 983    HUE -9.181693e-01  1.221064614 -1.562356e+00 -1.554486e+00 -1.492483e+00
## 984  NGRDI  8.760708e-03  0.010721637  1.787367e-03  8.883714e-03  1.697813e-02
## 985    Red  1.917166e+02 12.839919611  1.838418e+02  1.917551e+02  1.992398e+02
## 986    SCI -8.760708e-03  0.010721637 -1.697813e-02 -8.883714e-03 -1.787367e-03
## 987     SI  2.839748e-01  0.045120413  2.738891e-01  2.908836e-01  3.082561e-01
## 988   VARI  1.211667e-02  0.014837371  2.454060e-03  1.219110e-02  2.348303e-02
## 989    BGI  5.530584e-01  0.070546213  5.162736e-01  5.370370e-01  5.616927e-01
## 990     BI  1.636566e+02 15.838554294  1.579698e+02  1.650233e+02  1.709376e+02
## 991   Blue  1.023545e+02 19.386269513  9.268367e+01  1.005510e+02  1.077755e+02
## 992    GLI  1.184679e-01  0.033712880  1.154251e-01  1.264874e-01  1.365962e-01
## 993   gray  1.764643e+02 16.981708570  1.711931e+02  1.787695e+02  1.847959e+02
## 994  Green  1.847021e+02 19.405651011  1.799184e+02  1.880612e+02  1.943673e+02
## 995     HI  1.138675e+00  0.415889261  9.411413e-01  1.060355e+00  1.154928e+00
## 996    HUE  4.776940e-01  1.457560413 -1.546702e+00  1.549146e+00  1.562554e+00
## 997  NGRDI -1.195716e-02  0.033378550 -1.785921e-02 -6.830836e-03  6.244229e-03
## 998    Red  1.885476e+02 14.463469695  1.824490e+02  1.896122e+02  1.960204e+02
## 999    SCI  1.195716e-02  0.033378550 -6.244229e-03  6.830836e-03  1.785921e-02
## 1000    SI  3.011107e-01  0.054735114  2.879121e-01  3.094519e-01  3.306392e-01
## 1001  VARI -1.632520e-02  0.046416696 -2.416447e-02 -9.290173e-03  8.861186e-03
## 1002   BGI  5.520141e-01  0.062813968  5.161113e-01  5.406273e-01  5.711589e-01
## 1003    BI  1.704044e+02 14.084085540  1.610973e+02  1.696448e+02  1.790454e+02
## 1004  Blue  1.085908e+02 18.788523149  9.677551e+01  1.058980e+02  1.172857e+02
## 1005   GLI  1.323218e-01  0.020451757  1.255564e-01  1.350708e-01  1.441073e-01
## 1006  gray  1.846741e+02 14.015993053  1.753553e+02  1.842030e+02  1.936099e+02
## 1007 Green  1.956796e+02 13.874220670  1.864490e+02  1.955918e+02  2.048367e+02
## 1008    HI  9.170678e-01  0.084334210  8.595944e-01  9.310345e-01  9.787234e-01
## 1009   HUE -1.011148e+00  1.123121443 -1.562048e+00 -1.553444e+00 -1.516643e+00
## 1010 NGRDI  9.298746e-03  0.009423585  2.538820e-03  8.137282e-03  1.608670e-02
## 1011   Red  1.920764e+02 13.667670877  1.832449e+02  1.917959e+02  2.006939e+02
## 1012   SCI -9.298746e-03  0.009423585 -1.608670e-02 -8.137282e-03 -2.538820e-03
## 1013    SI  2.820562e-01  0.048708887  2.634109e-01  2.886659e-01  3.114409e-01
## 1014  VARI  1.293003e-02  0.013072203  3.470709e-03  1.107428e-02  2.210629e-02
## 1015   BGI  5.256734e-01  0.072080453  4.904160e-01  5.131542e-01  5.387520e-01
## 1016    BI  1.209879e+02 16.247767355  1.118147e+02  1.189464e+02  1.263970e+02
## 1017  Blue  7.622281e+01 19.336986929  6.736735e+01  7.324490e+01  7.971429e+01
## 1018   GLI  1.626774e-01  0.029979247  1.517999e-01  1.672948e-01  1.794422e-01
## 1019  gray  1.323620e+02 15.897821032  1.232632e+02  1.306054e+02  1.381737e+02
## 1020 Green  1.435045e+02 14.965749856  1.349796e+02  1.419184e+02  1.491735e+02
## 1021    HI  6.505509e-01  0.164303956  5.142857e-01  6.686013e-01  7.565742e-01
## 1022   HUE -1.506102e+00  0.403182575 -1.565822e+00 -1.564269e+00 -1.561532e+00
## 1023 NGRDI  4.373226e-02  0.022183631  2.795653e-02  4.204893e-02  6.274719e-02
## 1024   Red  1.318912e+02 17.594686655  1.206122e+02  1.299388e+02  1.397959e+02
## 1025   SCI -4.373226e-02  0.022183631 -6.274719e-02 -4.204893e-02 -2.795653e-02
## 1026    SI  2.736746e-01  0.053357396  2.541083e-01  2.808922e-01  3.038643e-01
## 1027  VARI  6.007716e-02  0.030307970  3.888750e-02  5.708035e-02  8.643853e-02
## 1028   BGI  5.578750e-01  0.060432132  5.296891e-01  5.460820e-01  5.657868e-01
## 1029    BI  1.735987e+02 12.539184577  1.677573e+02  1.740112e+02  1.801916e+02
## 1030  Blue  1.118281e+02 16.923042593  1.034694e+02  1.099592e+02  1.169388e+02
## 1031   GLI  1.329989e-01  0.020295599  1.279804e-01  1.369193e-01  1.437639e-01
## 1032  gray  1.882076e+02 12.446354665  1.826066e+02  1.890148e+02  1.951364e+02
## 1033 Green  1.997972e+02 12.252480796  1.942959e+02  2.009184e+02  2.067959e+02
## 1034    HI  8.807755e-01  0.078175032  8.305580e-01  8.645161e-01  9.274880e-01
## 1035   HUE -1.299025e+00  0.837040105 -1.563329e+00 -1.561718e+00 -1.553874e+00
## 1036 NGRDI  1.336452e-02  0.008493947  8.130490e-03  1.532367e-02  1.875696e-02
## 1037   Red  1.945761e+02 12.667674389  1.888878e+02  1.954286e+02  2.020408e+02
## 1038   SCI -1.336452e-02  0.008493947 -1.875696e-02 -1.532367e-02 -8.130490e-03
## 1039    SI  2.732726e-01  0.044168561  2.656649e-01  2.809121e-01  2.957317e-01
## 1040  VARI  1.858073e-02  0.011769841  1.119082e-02  2.138182e-02  2.583999e-02
## 1041   BGI  5.684252e-01  0.063482799  5.336771e-01  5.566303e-01  5.816006e-01
## 1042    BI  1.675780e+02 14.294929108  1.585796e+02  1.671015e+02  1.749552e+02
## 1043  Blue  1.091996e+02 18.916455546  9.734694e+01  1.065306e+02  1.158367e+02
## 1044   GLI  1.250669e-01  0.021061428  1.184196e-01  1.284107e-01  1.373935e-01
## 1045  gray  1.811104e+02 14.297603350  1.721679e+02  1.810355e+02  1.891966e+02
## 1046 Green  1.911642e+02 14.519567832  1.821020e+02  1.917551e+02  1.998980e+02
## 1047    HI  9.447771e-01  0.109967707  8.652215e-01  9.310345e-01  1.008479e+00
## 1048   HUE -6.989166e-01  1.356095320 -1.560914e+00 -1.552022e+00  1.406263e+00
## 1049 NGRDI  6.067767e-03  0.011733720 -9.096260e-04  7.880770e-03  1.491436e-02
## 1050   Red  1.887903e+02 13.471665480  1.803265e+02  1.885510e+02  1.964898e+02
## 1051   SCI -6.067767e-03  0.011733720 -1.491436e-02 -7.880770e-03  9.096260e-04
## 1052    SI  2.714593e-01  0.047930791  2.563863e-01  2.790943e-01  3.006797e-01
## 1053  VARI  8.537689e-03  0.016324603 -1.285990e-03  1.091068e-02  2.093258e-02
## 1054   BGI  5.538897e-01  0.064125987  5.183250e-01  5.382866e-01  5.640308e-01
## 1055    BI  1.658646e+02 14.583505573  1.572537e+02  1.636151e+02  1.724584e+02
## 1056  Blue  1.066650e+02 19.248572480  9.528571e+01  1.021429e+02  1.123673e+02
## 1057   GLI  1.363094e-01  0.022715745  1.297168e-01  1.413093e-01  1.501980e-01
## 1058  gray  1.799891e+02 14.437187462  1.715123e+02  1.781253e+02  1.867808e+02
## 1059 Green  1.915183e+02 14.304672360  1.831429e+02  1.899592e+02  1.985102e+02
## 1060    HI  8.562103e-01  0.101101371  7.977528e-01  8.248540e-01  9.136449e-01
## 1061   HUE -1.227100e+00  0.939637223 -1.564605e+00 -1.562888e+00 -1.555246e+00
## 1062 NGRDI  1.652142e-02  0.011335245  9.770929e-03  1.884648e-02  2.436599e-02
## 1063   Red  1.853111e+02 14.115508665  1.769184e+02  1.838980e+02  1.926531e+02
## 1064   SCI -1.652142e-02  0.011335245 -2.436599e-02 -1.884648e-02 -9.770929e-03
## 1065    SI  2.739631e-01  0.047236529  2.630824e-01  2.855556e-01  3.012643e-01
## 1066  VARI  2.290355e-02  0.015704551  1.366102e-02  2.663980e-02  3.336905e-02
## 1067   BGI  5.307067e-01  0.079491129  4.908226e-01  5.115637e-01  5.391858e-01
## 1068    BI  1.244050e+02 17.524930639  1.145777e+02  1.205029e+02  1.287368e+02
## 1069  Blue  7.965665e+01 22.016196402  6.855102e+01  7.406122e+01  8.216327e+01
## 1070   GLI  1.657628e-01  0.033222430  1.550760e-01  1.715281e-01  1.864473e-01
## 1071  gray  1.361650e+02 16.929042596  1.263868e+02  1.324612e+02  1.411490e+02
## 1072 Green  1.481796e+02 15.940682445  1.390204e+02  1.443776e+02  1.533367e+02
## 1073    HI  5.915352e-01  0.141259564  4.863329e-01  5.584580e-01  6.771488e-01
## 1074   HUE -1.545667e+00  0.229160113 -1.566612e+00 -1.565777e+00 -1.563666e+00
## 1075 NGRDI  5.114085e-02  0.021219066  3.613851e-02  5.408739e-02  6.786963e-02
## 1076   Red  1.341226e+02 17.920954201  1.229592e+02  1.310612e+02  1.401684e+02
## 1077   SCI -5.114085e-02  0.021219066 -6.786963e-02 -5.408739e-02 -3.613851e-02
## 1078    SI  2.630327e-01  0.054356949  2.480852e-01  2.730803e-01  2.915535e-01
## 1079  VARI  7.041398e-02  0.028409694  5.034989e-02  7.449017e-02  9.261343e-02
## 1080   BGI  5.090541e-01  0.071621979  4.742478e-01  4.918278e-01  5.171235e-01
## 1081    BI  1.546645e+02 13.854847481  1.473701e+02  1.535954e+02  1.598453e+02
## 1082  Blue  9.243691e+01 19.838070394  8.279592e+01  8.853061e+01  9.544388e+01
## 1083   GLI  1.502503e-01  0.025659272  1.416734e-01  1.544467e-01  1.651539e-01
## 1084  gray  1.686061e+02 13.449444388  1.615386e+02  1.679831e+02  1.743067e+02
## 1085 Green  1.802210e+02 12.955885865  1.731633e+02  1.799898e+02  1.859388e+02
## 1086    HI  8.772614e-01  0.125202746  7.808689e-01  8.820645e-01  9.664151e-01
## 1087   HUE -1.048378e+00  1.110732610 -1.564535e+00 -1.559310e+00 -1.530627e+00
## 1088 NGRDI  1.534138e-02  0.015740026  3.931639e-03  1.422708e-02  2.710640e-02
## 1089   Red  1.748448e+02 13.527314646  1.669388e+02  1.746735e+02  1.817500e+02
## 1090   SCI -1.534138e-02  0.015740026 -2.710640e-02 -1.422708e-02 -3.931639e-03
## 1091    SI  3.142759e-01  0.056796849  3.062803e-01  3.269907e-01  3.439769e-01
## 1092  VARI  2.072381e-02  0.021160936  5.361728e-03  1.921964e-02  3.683487e-02
## 1093   BGI  5.005302e-01  0.071717117  4.678733e-01  4.825143e-01  5.007282e-01
## 1094    BI  1.518064e+02 13.519412082  1.438607e+02  1.502683e+02  1.571903e+02
## 1095  Blue  9.037774e+01 19.070757928  8.095918e+01  8.640816e+01  9.316327e+01
## 1096   GLI  1.623223e-01  0.026338556  1.585465e-01  1.683177e-01  1.766429e-01
## 1097  gray  1.662064e+02 13.121014884  1.583341e+02  1.650341e+02  1.720948e+02
## 1098 Green  1.794100e+02 12.543613115  1.719592e+02  1.787143e+02  1.855051e+02
## 1099    HI  7.710813e-01  0.083588834  7.059590e-01  7.467045e-01  8.178881e-01
## 1100   HUE -1.532019e+00  0.291010205 -1.566422e+00 -1.565284e+00 -1.562901e+00
## 1101 NGRDI  2.961158e-02  0.011750087  2.125827e-02  3.067285e-02  3.940839e-02
## 1102   Red  1.691962e+02 13.394407166  1.605153e+02  1.681939e+02  1.759796e+02
## 1103   SCI -2.961158e-02  0.011750087 -3.940839e-02 -3.067285e-02 -2.125827e-02
## 1104    SI  3.091705e-01  0.053402042  3.045200e-01  3.221730e-01  3.352795e-01
## 1105  VARI  3.969639e-02  0.015437608  2.922158e-02  4.142549e-02  5.250423e-02
## 1106   BGI  4.943633e-01  0.077755608  4.569874e-01  4.762338e-01  5.018304e-01
## 1107    BI  1.500091e+02 16.346053182  1.388821e+02  1.478448e+02  1.580539e+02
## 1108  Blue  8.848824e+01 21.326640718  7.678571e+01  8.391837e+01  9.352041e+01
## 1109   GLI  1.644287e-01  0.029371844  1.578504e-01  1.702500e-01  1.807206e-01
## 1110  gray  1.642785e+02 16.145885123  1.530176e+02  1.624805e+02  1.731732e+02
## 1111 Green  1.774038e+02 15.624160188  1.666735e+02  1.760408e+02  1.867245e+02
## 1112    HI  7.767000e-01  0.116010100  6.838015e-01  7.543328e-01  8.530537e-01
## 1113   HUE -1.432486e+00  0.609356500 -1.566493e+00 -1.565250e+00 -1.561781e+00
## 1114 NGRDI  2.952168e-02  0.015972060  1.908002e-02  3.129810e-02  4.170809e-02
## 1115   Red  1.674074e+02 16.832797093  1.552857e+02  1.657755e+02  1.772041e+02
## 1116   SCI -2.952168e-02  0.015972060 -4.170809e-02 -3.129810e-02 -1.908002e-02
## 1117    SI  3.153788e-01  0.058775028  3.015591e-01  3.254717e-01  3.476195e-01
## 1118  VARI  3.938436e-02  0.021129887  2.549999e-02  4.173968e-02  5.583562e-02
## 1119   BGI  4.813056e-01  0.071723892  4.491575e-01  4.649947e-01  4.836746e-01
## 1120    BI  1.381362e+02 15.090175072  1.303772e+02  1.362351e+02  1.420290e+02
## 1121  Blue  8.110110e+01 19.585436620  7.206122e+01  7.751020e+01  8.260204e+01
## 1122   GLI  1.834788e-01  0.028294104  1.819230e-01  1.898909e-01  1.964345e-01
## 1123  gray  1.522604e+02 14.764932821  1.445142e+02  1.507554e+02  1.569166e+02
## 1124 Green  1.669542e+02 13.990913450  1.595000e+02  1.660816e+02  1.721633e+02
## 1125    HI  6.180147e-01  0.050472190  5.743553e-01  6.335472e-01  6.470588e-01
## 1126   HUE -1.566654e+00  0.001409423 -1.567265e+00 -1.566921e+00 -1.566494e+00
## 1127 NGRDI  5.238409e-02  0.010588912  4.844471e-02  5.247905e-02  6.001343e-02
## 1128   Red  1.505443e+02 15.296378341  1.422653e+02  1.485510e+02  1.554898e+02
## 1129   SCI -5.238409e-02  0.010588912 -6.001343e-02 -5.247905e-02 -4.844471e-02
## 1130    SI  3.065535e-01  0.051767056  2.973581e-01  3.166563e-01  3.327070e-01
## 1131  VARI  6.974471e-02  0.013018130  6.419647e-02  6.901146e-02  7.995474e-02
## 1132   BGI  5.181075e-01  0.068363670  4.873843e-01  5.059568e-01  5.272023e-01
## 1133    BI  1.163349e+02 16.070112835  1.088619e+02  1.140037e+02  1.194544e+02
## 1134  Blue  7.468722e+01 18.778085672  6.746939e+01  7.146939e+01  7.546939e+01
## 1135   GLI  1.914194e-01  0.030226781  1.887478e-01  1.971280e-01  2.047002e-01
## 1136  gray  1.283932e+02 15.739239594  1.206865e+02  1.262927e+02  1.322926e+02
## 1137 Green  1.428105e+02 14.813464029  1.352245e+02  1.411224e+02  1.472449e+02
## 1138    HI  3.431670e-01  0.096389971  2.647059e-01  3.538462e-01  4.052184e-01
## 1139   HUE -1.566987e+00  0.001271632 -1.567413e+00 -1.567244e+00 -1.566957e+00
## 1140 NGRDI  8.631994e-02  0.017657830  8.039976e-02  8.675018e-02  9.857390e-02
## 1141   Red  1.205654e+02 17.177782156  1.116122e+02  1.176939e+02  1.251224e+02
## 1142   SCI -8.631994e-02  0.017657830 -9.857390e-02 -8.675018e-02 -8.039976e-02
## 1143    SI  2.404711e-01  0.044615347  2.236065e-01  2.449146e-01  2.644985e-01
## 1144  VARI  1.195189e-01  0.023396586  1.102392e-01  1.186167e-01  1.375628e-01
## 1145   BGI  4.977048e-01  0.071900823  4.658040e-01  4.803104e-01  5.011048e-01
## 1146    BI  1.500779e+02 13.501297581  1.426232e+02  1.483246e+02  1.558315e+02
## 1147  Blue  8.978499e+01 19.156292216  8.053061e+01  8.559184e+01  9.301531e+01
## 1148   GLI  1.707078e-01  0.027092189  1.662892e-01  1.768374e-01  1.846372e-01
## 1149  gray  1.647727e+02 13.013847383  1.573909e+02  1.634205e+02  1.710752e+02
## 1150 Green  1.791654e+02 12.274127833  1.720816e+02  1.782245e+02  1.857755e+02
## 1151    HI  6.850856e-01  0.068881595  6.386950e-01  6.750554e-01  6.842105e-01
## 1152   HUE -1.564609e+00  0.059978148 -1.567163e+00 -1.566854e+00 -1.566082e+00
## 1153 NGRDI  4.124948e-02  0.011068541  3.834929e-02  4.424936e-02  4.884655e-02
## 1154   Red  1.651073e+02 13.317742650  1.571020e+02  1.638878e+02  1.718776e+02
## 1155   SCI -4.124948e-02  0.011068541 -4.884655e-02 -4.424936e-02 -3.834929e-02
## 1156    SI  3.012645e-01  0.052454473  2.927425e-01  3.124210e-01  3.277086e-01
## 1157  VARI  5.540018e-02  0.014143176  5.204514e-02  5.907512e-02  6.517622e-02
## 1158   BGI  5.253363e-01  0.067629035  4.936205e-01  5.123868e-01  5.341050e-01
## 1159    BI  1.611653e+02 13.578761491  1.538553e+02  1.605841e+02  1.673491e+02
## 1160  Blue  9.921314e+01 19.003533597  8.944898e+01  9.644898e+01  1.039592e+02
## 1161   GLI  1.471165e-01  0.024127075  1.394103e-01  1.508226e-01  1.603053e-01
## 1162  gray  1.755543e+02 13.299696296  1.682493e+02  1.753822e+02  1.821610e+02
## 1163 Green  1.877050e+02 12.918404180  1.806735e+02  1.877551e+02  1.946735e+02
## 1164    HI  8.432663e-01  0.116994830  7.273714e-01  8.486218e-01  9.324234e-01
## 1165   HUE -1.256189e+00  0.890806511 -1.565558e+00 -1.562681e+00 -1.552513e+00
## 1166 NGRDI  1.891074e-02  0.014359333  8.185311e-03  1.891443e-02  3.036426e-02
## 1167   Red  1.808066e+02 13.434965099  1.733469e+02  1.805510e+02  1.878980e+02
## 1168   SCI -1.891074e-02  0.014359333 -3.036426e-02 -1.891443e-02 -8.185311e-03
## 1169    SI  2.964117e-01  0.053092933  2.850698e-01  3.045847e-01  3.243282e-01
## 1170  VARI  2.584586e-02  0.019483439  1.112625e-02  2.565829e-02  4.159864e-02
## 1171   BGI  4.909821e-01  0.076433300  4.546185e-01  4.741245e-01  4.946815e-01
## 1172    BI  1.316202e+02 16.319855797  1.219246e+02  1.285912e+02  1.369749e+02
## 1173  Blue  7.893557e+01 20.421924398  6.875510e+01  7.459184e+01  8.120408e+01
## 1174   GLI  1.828602e-01  0.031902343  1.774208e-01  1.898081e-01  1.998493e-01
## 1175  gray  1.449903e+02 15.978123021  1.352068e+02  1.422197e+02  1.511551e+02
## 1176 Green  1.591347e+02 15.143668444  1.496071e+02  1.568367e+02  1.657755e+02
## 1177    HI  5.835302e-01  0.087230938  5.233495e-01  5.755921e-01  6.446344e-01
## 1178   HUE -1.565185e+00  0.056844131 -1.567252e+00 -1.566854e+00 -1.566054e+00
## 1179 NGRDI  5.660431e-02  0.016043690  4.637541e-02  5.825661e-02  6.869171e-02
## 1180   Red  1.424065e+02 17.029333387  1.319592e+02  1.393980e+02  1.489796e+02
## 1181   SCI -5.660431e-02  0.016043690 -6.869171e-02 -5.825661e-02 -4.637541e-02
## 1182    SI  2.940035e-01  0.052286143  2.846082e-01  3.037771e-01  3.223045e-01
## 1183  VARI  7.584273e-02  0.020423375  6.218717e-02  7.792345e-02  9.096605e-02
## 1184   BGI  4.736437e-01  0.072212077  4.361223e-01  4.614656e-01  4.888106e-01
## 1185    BI  1.446258e+02 14.468062144  1.359823e+02  1.436407e+02  1.511702e+02
## 1186  Blue  8.342288e+01 19.322375240  7.302041e+01  8.069388e+01  8.867857e+01
## 1187   GLI  1.833963e-01  0.028569623  1.757036e-01  1.884002e-01  1.992038e-01
## 1188  gray  1.594152e+02 14.231637535  1.507813e+02  1.588291e+02  1.666201e+02
## 1189 Green  1.745284e+02 13.460947280  1.664031e+02  1.743980e+02  1.819184e+02
## 1190    HI  6.532066e-01  0.041206364  6.379420e-01  6.459620e-01  6.774194e-01
## 1191   HUE -1.566672e+00  0.005955030 -1.567267e+00 -1.567020e+00 -1.566662e+00
## 1192 NGRDI  4.800437e-02  0.009296472  4.393461e-02  4.901220e-02  5.308099e-02
## 1193   Red  1.587183e+02 14.569975564  1.494898e+02  1.578980e+02  1.662245e+02
## 1194   SCI -4.800437e-02  0.009296472 -5.308099e-02 -4.901220e-02 -4.393461e-02
## 1195    SI  3.179923e-01  0.055246255  3.010899e-01  3.238763e-01  3.483207e-01
## 1196  VARI  6.348123e-02  0.010905239  5.866035e-02  6.449864e-02  6.898476e-02
## 1197   BGI  5.509069e-01  0.065439595  5.162548e-01  5.366734e-01  5.652501e-01
## 1198    BI  1.575559e+02 14.935285964  1.493091e+02  1.580308e+02  1.656656e+02
## 1199  Blue  9.839235e+01 19.698069087  8.722959e+01  9.608163e+01  1.049745e+02
## 1200   GLI  1.175620e-01  0.021738963  1.072494e-01  1.197379e-01  1.317572e-01
## 1201  gray  1.697889e+02 15.520961712  1.611838e+02  1.708662e+02  1.792393e+02
## 1202 Green  1.774054e+02 17.056276178  1.672908e+02  1.789796e+02  1.888980e+02
## 1203    HI  1.127089e+00  0.213384041  9.629172e-01  1.138308e+00  1.271128e+00
## 1204   HUE  6.361729e-01  1.410905041 -1.534243e+00  1.560143e+00  1.565094e+00
## 1205 NGRDI -1.408290e-02  0.023231293 -3.004887e-02 -1.500344e-02  4.101386e-03
## 1206   Red  1.820576e+02 12.774441026  1.753316e+02  1.827347e+02  1.891837e+02
## 1207   SCI  1.408290e-02  0.023231293 -4.101386e-03  1.500344e-02  3.004887e-02
## 1208    SI  3.041629e-01  0.058549704  2.835034e-01  3.125746e-01  3.388524e-01
## 1209  VARI -1.875302e-02  0.031458960 -4.064677e-02 -2.066285e-02  5.830924e-03
## 1210   BGI  4.603501e-01  0.066690415  4.293498e-01  4.464923e-01  4.688840e-01
## 1211    BI  1.369996e+02 12.903926346  1.303857e+02  1.353736e+02  1.406537e+02
## 1212  Blue  7.717352e+01 17.128535412  6.948980e+01  7.432653e+01  7.971429e+01
## 1213   GLI  1.907362e-01  0.027658058  1.854010e-01  1.970940e-01  2.050209e-01
## 1214  gray  1.513755e+02 12.533123287  1.447472e+02  1.500102e+02  1.555212e+02
## 1215 Green  1.664320e+02 11.542724972  1.603265e+02  1.656122e+02  1.709388e+02
## 1216    HI  6.338923e-01  0.090799056  5.515404e-01  6.348096e-01  6.772152e-01
## 1217   HUE -1.548845e+00  0.229626368 -1.567450e+00 -1.567049e+00 -1.566466e+00
## 1218 NGRDI  5.237126e-02  0.014917541  4.633257e-02  5.440053e-02  6.384365e-02
## 1219   Red  1.501077e+02 13.853210365  1.422857e+02  1.477755e+02  1.547959e+02
## 1220   SCI -5.237126e-02  0.014917541 -6.384365e-02 -5.440053e-02 -4.633257e-02
## 1221    SI  3.263082e-01  0.050926985  3.113899e-01  3.341239e-01  3.550033e-01
## 1222  VARI  6.881538e-02  0.019124398  6.061852e-02  7.061930e-02  8.483172e-02
## 1223   BGI  4.945712e-01  0.072534243  4.608673e-01  4.801561e-01  5.029688e-01
## 1224    BI  1.355914e+02 15.327820824  1.282724e+02  1.341147e+02  1.408786e+02
## 1225  Blue  8.048875e+01 19.806457644  7.151020e+01  7.730612e+01  8.369388e+01
## 1226   GLI  1.677679e-01  0.028555953  1.594224e-01  1.741036e-01  1.847201e-01
## 1227  gray  1.486683e+02 15.112120934  1.414012e+02  1.476821e+02  1.546591e+02
## 1228 Green  1.610853e+02 14.800418939  1.540408e+02  1.610612e+02  1.678367e+02
## 1229    HI  7.347673e-01  0.140129855  6.384710e-01  6.915866e-01  8.122867e-01
## 1230   HUE -1.383908e+00  0.711218484 -1.566389e+00 -1.565415e+00 -1.561489e+00
## 1231 NGRDI  3.506482e-02  0.019472248  2.233800e-02  3.980236e-02  4.909028e-02
## 1232   Red  1.502860e+02 15.355172926  1.422245e+02  1.482857e+02  1.566327e+02
## 1233   SCI -3.506482e-02  0.019472248 -4.909028e-02 -3.980236e-02 -2.233800e-02
## 1234    SI  3.096930e-01  0.056438616  2.932626e-01  3.152297e-01  3.387922e-01
## 1235  VARI  4.701988e-02  0.025845249  3.067382e-02  5.345882e-02  6.551386e-02
## 1236   BGI  4.833572e-01  0.076549012  4.456626e-01  4.703528e-01  4.968566e-01
## 1237    BI  1.332715e+02 16.075478052  1.247668e+02  1.311760e+02  1.386993e+02
## 1238  Blue  7.767911e+01 20.781556650  6.732653e+01  7.412245e+01  8.144898e+01
## 1239   GLI  1.719859e-01  0.029334902  1.630791e-01  1.766150e-01  1.883165e-01
## 1240  gray  1.462727e+02 15.829454682  1.378049e+02  1.446074e+02  1.523001e+02
## 1241 Green  1.587213e+02 15.267577895  1.504490e+02  1.576327e+02  1.653265e+02
## 1242    HI  7.344640e-01  0.141404219  6.357214e-01  7.025882e-01  8.295425e-01
## 1243   HUE -1.397312e+00  0.682988251 -1.566325e+00 -1.565095e+00 -1.560846e+00
## 1244 NGRDI  3.562392e-02  0.019778881  2.172519e-02  3.921069e-02  4.992249e-02
## 1245   Red  1.479862e+02 16.363214380  1.385918e+02  1.457551e+02  1.546327e+02
## 1246   SCI -3.562392e-02  0.019778881 -4.992249e-02 -3.921069e-02 -2.172519e-02
## 1247    SI  3.199480e-01  0.062886283  2.954565e-01  3.264114e-01  3.563706e-01
## 1248  VARI  4.751978e-02  0.026222598  2.910383e-02  5.226047e-02  6.626938e-02
## 1249   BGI  4.891723e-01  0.077124038  4.502185e-01  4.718030e-01  4.980867e-01
## 1250    BI  1.511301e+02 15.085195539  1.423862e+02  1.496438e+02  1.573360e+02
## 1251  Blue  8.899860e+01 21.120474811  7.759184e+01  8.475510e+01  9.359184e+01
## 1252   GLI  1.718740e-01  0.028383481  1.672119e-01  1.778123e-01  1.866563e-01
## 1253  gray  1.659428e+02 14.691293244  1.572901e+02  1.649439e+02  1.727401e+02
## 1254 Green  1.802973e+02 14.015851600  1.719796e+02  1.797551e+02  1.876735e+02
## 1255    HI  7.107380e-01  0.049556763  6.790805e-01  6.962406e-01  7.156105e-01
## 1256   HUE -1.565891e+00  0.002488825 -1.566880e+00 -1.566620e+00 -1.565975e+00
## 1257 NGRDI  3.833134e-02  0.008556742  3.585884e-02  4.100876e-02  4.359573e-02
## 1258   Red  1.670983e+02 14.538445320  1.586327e+02  1.662041e+02  1.738980e+02
## 1259   SCI -3.833134e-02  0.008556742 -4.359573e-02 -4.100876e-02 -3.585884e-02
## 1260    SI  3.123070e-01  0.057964673  2.994342e-01  3.240924e-01  3.440454e-01
## 1261  VARI  5.109758e-02  0.010514036  4.851043e-02  5.457916e-02  5.762141e-02
## 1262   BGI  5.497641e-01  0.071990678  5.051916e-01  5.345074e-01  5.746432e-01
## 1263    BI  1.592227e+02 15.343947347  1.515961e+02  1.589253e+02  1.661636e+02
## 1264  Blue  9.815995e+01 20.578510863  8.644898e+01  9.457143e+01  1.044694e+02
## 1265   GLI  1.106292e-01  0.025172084  1.020395e-01  1.158511e-01  1.265604e-01
## 1266  gray  1.710800e+02 15.796697661  1.636931e+02  1.713225e+02  1.786709e+02
## 1267 Green  1.774539e+02 16.914863703  1.702653e+02  1.781837e+02  1.857143e+02
## 1268    HI  1.240187e+00  0.268503292  1.141919e+00  1.215232e+00  1.304976e+00
## 1269   HUE  1.223562e+00  0.964983504  1.561161e+00  1.564360e+00  1.566215e+00
## 1270 NGRDI -2.556116e-02  0.023643060 -3.449972e-02 -2.424276e-02 -1.622224e-02
## 1271   Red  1.863689e+02 13.917131854  1.789592e+02  1.869184e+02  1.942245e+02
## 1272   SCI  2.556116e-02  0.023643060  1.622224e-02  2.424276e-02  3.449972e-02
## 1273    SI  3.160340e-01  0.061573889  2.956308e-01  3.276614e-01  3.538531e-01
## 1274  VARI -3.446801e-02  0.032521555 -4.624071e-02 -3.279446e-02 -2.202713e-02
## 1275   BGI  5.551954e-01  0.060746322  5.231954e-01  5.460024e-01  5.712243e-01
## 1276    BI  1.661646e+02 14.931612821  1.569303e+02  1.664568e+02  1.747483e+02
## 1277  Blue  1.042867e+02 19.142136682  9.310204e+01  1.024898e+02  1.119184e+02
## 1278   GLI  1.156305e-01  0.019603682  1.054500e-01  1.165262e-01  1.280371e-01
## 1279  gray  1.789397e+02 15.175842212  1.695171e+02  1.797403e+02  1.882576e+02
## 1280 Green  1.866665e+02 15.709198703  1.768163e+02  1.877347e+02  1.970918e+02
## 1281    HI  1.136177e+00  0.179695391  1.006772e+00  1.152008e+00  1.262136e+00
## 1282   HUE  8.152243e-01  1.315047653  1.375514e+00  1.561724e+00  1.565548e+00
## 1283 NGRDI -1.503247e-02  0.019851187 -2.870132e-02 -1.640505e-02 -7.652383e-04
## 1284   Red  1.922333e+02 14.629418358  1.832245e+02  1.923265e+02  2.014898e+02
## 1285   SCI  1.503247e-02  0.019851187  7.652383e-04  1.640505e-02  2.870132e-02
## 1286    SI  3.012859e-01  0.053649145  2.808378e-01  3.067718e-01  3.314434e-01
## 1287  VARI -2.023670e-02  0.026859109 -3.897291e-02 -2.256197e-02 -1.041628e-03
## 1288   BGI  5.782218e-01  0.073713618  5.328897e-01  5.679634e-01  6.076278e-01
## 1289    BI  1.531340e+02 20.303029478  1.416983e+02  1.542746e+02  1.660485e+02
## 1290  Blue  9.713375e+01 22.574468320  8.230612e+01  9.493878e+01  1.087143e+02
## 1291   GLI  8.987709e-02  0.031091971  7.255340e-02  9.339408e-02  1.115092e-01
## 1292  gray  1.632016e+02 21.773797084  1.513917e+02  1.650409e+02  1.775392e+02
## 1293 Green  1.668868e+02 24.228789246  1.538980e+02  1.691633e+02  1.834592e+02
## 1294    HI  1.458850e+00  0.447086283  1.158589e+00  1.417849e+00  1.683580e+00
## 1295   HUE  1.107249e+00  1.096934808  1.560294e+00  1.566651e+00  1.568067e+00
## 1296 NGRDI -4.370844e-02  0.039046882 -6.815533e-02 -4.256342e-02 -1.584418e-02
## 1297   Red  1.811563e+02 19.653342033  1.704694e+02  1.823878e+02  1.941020e+02
## 1298   SCI  4.370844e-02  0.039046882  1.584418e-02  4.256342e-02  6.815533e-02
## 1299    SI  3.092505e-01  0.068714780  2.721891e-01  3.173554e-01  3.538793e-01
## 1300  VARI -5.934955e-02  0.052935406 -9.209065e-02 -5.845817e-02 -2.228588e-02
## 1301   BGI  4.578249e-01  0.069788671  4.253275e-01  4.455446e-01  4.685013e-01
## 1302    BI  1.394011e+02 13.902080948  1.307526e+02  1.376127e+02  1.459149e+02
## 1303  Blue  7.836742e+01 18.221380826  6.916327e+01  7.551020e+01  8.267347e+01
## 1304   GLI  1.932495e-01  0.028192742  1.870605e-01  1.981824e-01  2.075384e-01
## 1305  gray  1.541359e+02 13.670509813  1.453141e+02  1.525849e+02  1.613091e+02
## 1306 Green  1.697594e+02 12.891990425  1.612857e+02  1.686939e+02  1.772041e+02
## 1307    HI  6.182237e-01  0.057107968  5.581872e-01  6.381407e-01  6.518657e-01
## 1308   HUE -1.567001e+00  0.002008998 -1.567533e+00 -1.567223e+00 -1.566934e+00
## 1309 NGRDI  5.476766e-02  0.011487292  4.871060e-02  5.427046e-02  6.345700e-02
## 1310   Red  1.523520e+02 14.447575699  1.427551e+02  1.505102e+02  1.602857e+02
## 1311   SCI -5.476766e-02  0.011487292 -6.345700e-02 -5.427046e-02 -4.871060e-02
## 1312    SI  3.269492e-01  0.052396085  3.131143e-01  3.343954e-01  3.537519e-01
## 1313  VARI  7.183425e-02  0.014044639  6.398123e-02  7.022425e-02  8.389617e-02
## 1314   BGI  5.433003e-01  0.080509769  5.003178e-01  5.260650e-01  5.603382e-01
## 1315    BI  1.229925e+02 22.676941957  1.083390e+02  1.180642e+02  1.339646e+02
## 1316  Blue  7.443487e+01 24.700586500  6.047449e+01  6.772449e+01  7.991837e+01
## 1317   GLI  1.002194e-01  0.028803679  8.636963e-02  1.018091e-01  1.184094e-01
## 1318  gray  1.315358e+02 24.166978328  1.156010e+02  1.263858e+02  1.441172e+02
## 1319 Green  1.351380e+02 26.769994709  1.171224e+02  1.293980e+02  1.495714e+02
## 1320    HI  1.412909e+00  0.343236318  1.213558e+00  1.441452e+00  1.625032e+00
## 1321   HUE  1.141374e+00  1.061235025  1.560271e+00  1.565005e+00  1.566374e+00
## 1322 NGRDI -4.408670e-02  0.034088184 -6.872650e-02 -4.979960e-02 -2.280517e-02
## 1323   Red  1.462348e+02 20.249014525  1.331224e+02  1.430408e+02  1.577347e+02
## 1324   SCI  4.408670e-02  0.034088184  2.280517e-02  4.979960e-02  6.872650e-02
## 1325    SI  3.380381e-01  0.073130513  3.153315e-01  3.549401e-01  3.811566e-01
## 1326  VARI -5.851747e-02  0.045732819 -9.082683e-02 -6.616031e-02 -3.099298e-02
## 1327   BGI  4.950562e-01  0.075654157  4.563590e-01  4.833557e-01  5.115477e-01
## 1328    BI  1.306872e+02 17.507306667  1.202224e+02  1.289388e+02  1.384521e+02
## 1329  Blue  7.607665e+01 21.258945133  6.471429e+01  7.250000e+01  8.136735e+01
## 1330   GLI  1.493519e-01  0.031952196  1.302149e-01  1.524699e-01  1.723624e-01
## 1331  gray  1.423360e+02 18.051337428  1.308762e+02  1.407138e+02  1.516943e+02
## 1332 Green  1.516844e+02 19.328922610  1.383418e+02  1.501020e+02  1.637806e+02
## 1333    HI  9.545467e-01  0.229851933  7.446127e-01  9.392129e-01  1.141102e+00
## 1334   HUE -2.372749e-01  1.524993615 -1.564403e+00 -1.540947e+00  1.556133e+00
## 1335 NGRDI  6.915608e-03  0.029070267 -1.673489e-02  7.660257e-03  3.204692e-02
## 1336   Red  1.492458e+02 16.165977805  1.402449e+02  1.480408e+02  1.563724e+02
## 1337   SCI -6.915608e-03  0.029070267 -3.204692e-02 -7.660257e-03  1.673489e-02
## 1338    SI  3.345940e-01  0.063954079  3.116501e-01  3.420964e-01  3.707661e-01
## 1339  VARI  9.392848e-03  0.038543776 -2.224237e-02  1.030962e-02  4.327312e-02
## 1340   BGI  4.825232e-01  0.064109709  4.487681e-01  4.695543e-01  4.968354e-01
## 1341    BI  1.589125e+02 14.604421080  1.490106e+02  1.565937e+02  1.667296e+02
## 1342  Blue  9.097271e+01 17.795859455  8.085714e+01  8.736735e+01  9.642857e+01
## 1343   GLI  1.638030e-01  0.024559347  1.539416e-01  1.678815e-01  1.793575e-01
## 1344  gray  1.740549e+02 14.628133723  1.640534e+02  1.719860e+02  1.822361e+02
## 1345 Green  1.874722e+02 13.953248417  1.780204e+02  1.859388e+02  1.955306e+02
## 1346    HI  8.278611e-01  0.142537201  7.082585e-01  8.025809e-01  9.149619e-01
## 1347   HUE -1.132381e+00  1.066448924 -1.566595e+00 -1.564801e+00 -1.557562e+00
## 1348 NGRDI  2.281530e-02  0.019125184  1.083953e-02  2.537253e-02  3.903968e-02
## 1349   Red  1.793906e+02 16.886961273  1.672857e+02  1.768980e+02  1.891429e+02
## 1350   SCI -2.281530e-02  0.019125184 -3.903968e-02 -2.537253e-02 -1.083953e-02
## 1351    SI  3.311142e-01  0.054800879  3.115736e-01  3.378747e-01  3.635422e-01
## 1352  VARI  3.042245e-02  0.025250191  1.462237e-02  3.390225e-02  5.215949e-02
## 1353   BGI  5.079571e-01  0.069477455  4.733950e-01  4.951851e-01  5.198283e-01
## 1354    BI  1.443206e+02 15.621134529  1.345758e+02  1.435821e+02  1.523447e+02
## 1355  Blue  8.561669e+01 19.784450282  7.467347e+01  8.279592e+01  9.114286e+01
## 1356   GLI  1.450213e-01  0.025913335  1.331806e-01  1.481585e-01  1.618094e-01
## 1357  gray  1.570285e+02 15.900702841  1.469231e+02  1.567712e+02  1.661186e+02
## 1358 Green  1.670401e+02 16.587756186  1.564082e+02  1.673265e+02  1.774592e+02
## 1359    HI  9.460817e-01  0.183930315  7.989478e-01  9.359734e-01  1.084247e+00
## 1360   HUE -3.656883e-01  1.497186552 -1.563539e+00 -1.547094e+00  1.551803e+00
## 1361 NGRDI  6.913620e-03  0.022677370 -9.986760e-03  7.851718e-03  2.507888e-02
## 1362   Red  1.646008e+02 14.992481853  1.548980e+02  1.640612e+02  1.731837e+02
## 1363   SCI -6.913620e-03  0.022677370 -2.507888e-02 -7.851718e-03  9.986760e-03
## 1364    SI  3.224781e-01  0.058898945  3.040703e-01  3.306876e-01  3.551841e-01
## 1365  VARI  9.564455e-03  0.030336141 -1.343971e-02  1.055493e-02  3.411655e-02
##      file     ImageJ LeafDoctor APSAssess        sev
## 1       1 26.7800000      27.16     26.11 26.7800000
## 2       1 26.7800000      27.16     26.11 26.7800000
## 3       1 26.7800000      27.16     26.11 26.7800000
## 4       1 26.7800000      27.16     26.11 26.7800000
## 5       1 26.7800000      27.16     26.11 26.7800000
## 6       1 26.7800000      27.16     26.11 26.7800000
## 7       1 26.7800000      27.16     26.11 26.7800000
## 8       1 26.7800000      27.16     26.11 26.7800000
## 9       1 26.7800000      27.16     26.11 26.7800000
## 10      1 26.7800000      27.16     26.11 26.7800000
## 11      1 26.7800000      27.16     26.11 26.7800000
## 12      1 26.7800000      27.16     26.11 26.7800000
## 13      1 26.7800000      27.16     26.11 26.7800000
## 14     10 24.3200000      24.17     23.39 24.3200000
## 15     10 24.3200000      24.17     23.39 24.3200000
## 16     10 24.3200000      24.17     23.39 24.3200000
## 17     10 24.3200000      24.17     23.39 24.3200000
## 18     10 24.3200000      24.17     23.39 24.3200000
## 19     10 24.3200000      24.17     23.39 24.3200000
## 20     10 24.3200000      24.17     23.39 24.3200000
## 21     10 24.3200000      24.17     23.39 24.3200000
## 22     10 24.3200000      24.17     23.39 24.3200000
## 23     10 24.3200000      24.17     23.39 24.3200000
## 24     10 24.3200000      24.17     23.39 24.3200000
## 25     10 24.3200000      24.17     23.39 24.3200000
## 26     10 24.3200000      24.17     23.39 24.3200000
## 27     11 16.3100000      15.79     15.81 16.3100000
## 28     11 16.3100000      15.79     15.81 16.3100000
## 29     11 16.3100000      15.79     15.81 16.3100000
## 30     11 16.3100000      15.79     15.81 16.3100000
## 31     11 16.3100000      15.79     15.81 16.3100000
## 32     11 16.3100000      15.79     15.81 16.3100000
## 33     11 16.3100000      15.79     15.81 16.3100000
## 34     11 16.3100000      15.79     15.81 16.3100000
## 35     11 16.3100000      15.79     15.81 16.3100000
## 36     11 16.3100000      15.79     15.81 16.3100000
## 37     11 16.3100000      15.79     15.81 16.3100000
## 38     11 16.3100000      15.79     15.81 16.3100000
## 39     11 16.3100000      15.79     15.81 16.3100000
## 40     12 14.8100000      14.36     14.93 14.8100000
## 41     12 14.8100000      14.36     14.93 14.8100000
## 42     12 14.8100000      14.36     14.93 14.8100000
## 43     12 14.8100000      14.36     14.93 14.8100000
## 44     12 14.8100000      14.36     14.93 14.8100000
## 45     12 14.8100000      14.36     14.93 14.8100000
## 46     12 14.8100000      14.36     14.93 14.8100000
## 47     12 14.8100000      14.36     14.93 14.8100000
## 48     12 14.8100000      14.36     14.93 14.8100000
## 49     12 14.8100000      14.36     14.93 14.8100000
## 50     12 14.8100000      14.36     14.93 14.8100000
## 51     12 14.8100000      14.36     14.93 14.8100000
## 52     12 14.8100000      14.36     14.93 14.8100000
## 53    126  7.9200000       8.05      8.09  7.9200000
## 54    126  7.9200000       8.05      8.09  7.9200000
## 55    126  7.9200000       8.05      8.09  7.9200000
## 56    126  7.9200000       8.05      8.09  7.9200000
## 57    126  7.9200000       8.05      8.09  7.9200000
## 58    126  7.9200000       8.05      8.09  7.9200000
## 59    126  7.9200000       8.05      8.09  7.9200000
## 60    126  7.9200000       8.05      8.09  7.9200000
## 61    126  7.9200000       8.05      8.09  7.9200000
## 62    126  7.9200000       8.05      8.09  7.9200000
## 63    126  7.9200000       8.05      8.09  7.9200000
## 64    126  7.9200000       8.05      8.09  7.9200000
## 65    126  7.9200000       8.05      8.09  7.9200000
## 66    127  9.4800000      10.28      9.30  9.4800000
## 67    127  9.4800000      10.28      9.30  9.4800000
## 68    127  9.4800000      10.28      9.30  9.4800000
## 69    127  9.4800000      10.28      9.30  9.4800000
## 70    127  9.4800000      10.28      9.30  9.4800000
## 71    127  9.4800000      10.28      9.30  9.4800000
## 72    127  9.4800000      10.28      9.30  9.4800000
## 73    127  9.4800000      10.28      9.30  9.4800000
## 74    127  9.4800000      10.28      9.30  9.4800000
## 75    127  9.4800000      10.28      9.30  9.4800000
## 76    127  9.4800000      10.28      9.30  9.4800000
## 77    127  9.4800000      10.28      9.30  9.4800000
## 78    127  9.4800000      10.28      9.30  9.4800000
## 79    128  9.3900000       9.69      6.72  9.3900000
## 80    128  9.3900000       9.69      6.72  9.3900000
## 81    128  9.3900000       9.69      6.72  9.3900000
## 82    128  9.3900000       9.69      6.72  9.3900000
## 83    128  9.3900000       9.69      6.72  9.3900000
## 84    128  9.3900000       9.69      6.72  9.3900000
## 85    128  9.3900000       9.69      6.72  9.3900000
## 86    128  9.3900000       9.69      6.72  9.3900000
## 87    128  9.3900000       9.69      6.72  9.3900000
## 88    128  9.3900000       9.69      6.72  9.3900000
## 89    128  9.3900000       9.69      6.72  9.3900000
## 90    128  9.3900000       9.69      6.72  9.3900000
## 91    128  9.3900000       9.69      6.72  9.3900000
## 92    129  0.4900000       0.83      0.32  0.4900000
## 93    129  0.4900000       0.83      0.32  0.4900000
## 94    129  0.4900000       0.83      0.32  0.4900000
## 95    129  0.4900000       0.83      0.32  0.4900000
## 96    129  0.4900000       0.83      0.32  0.4900000
## 97    129  0.4900000       0.83      0.32  0.4900000
## 98    129  0.4900000       0.83      0.32  0.4900000
## 99    129  0.4900000       0.83      0.32  0.4900000
## 100   129  0.4900000       0.83      0.32  0.4900000
## 101   129  0.4900000       0.83      0.32  0.4900000
## 102   129  0.4900000       0.83      0.32  0.4900000
## 103   129  0.4900000       0.83      0.32  0.4900000
## 104   129  0.4900000       0.83      0.32  0.4900000
## 105    13 13.6400000      13.93     13.67 13.6400000
## 106    13 13.6400000      13.93     13.67 13.6400000
## 107    13 13.6400000      13.93     13.67 13.6400000
## 108    13 13.6400000      13.93     13.67 13.6400000
## 109    13 13.6400000      13.93     13.67 13.6400000
## 110    13 13.6400000      13.93     13.67 13.6400000
## 111    13 13.6400000      13.93     13.67 13.6400000
## 112    13 13.6400000      13.93     13.67 13.6400000
## 113    13 13.6400000      13.93     13.67 13.6400000
## 114    13 13.6400000      13.93     13.67 13.6400000
## 115    13 13.6400000      13.93     13.67 13.6400000
## 116    13 13.6400000      13.93     13.67 13.6400000
## 117    13 13.6400000      13.93     13.67 13.6400000
## 118   130 47.7800000      47.82     46.43 47.7800000
## 119   130 47.7800000      47.82     46.43 47.7800000
## 120   130 47.7800000      47.82     46.43 47.7800000
## 121   130 47.7800000      47.82     46.43 47.7800000
## 122   130 47.7800000      47.82     46.43 47.7800000
## 123   130 47.7800000      47.82     46.43 47.7800000
## 124   130 47.7800000      47.82     46.43 47.7800000
## 125   130 47.7800000      47.82     46.43 47.7800000
## 126   130 47.7800000      47.82     46.43 47.7800000
## 127   130 47.7800000      47.82     46.43 47.7800000
## 128   130 47.7800000      47.82     46.43 47.7800000
## 129   130 47.7800000      47.82     46.43 47.7800000
## 130   130 47.7800000      47.82     46.43 47.7800000
## 131   131  0.7800000       1.44      0.23  0.7800000
## 132   131  0.7800000       1.44      0.23  0.7800000
## 133   131  0.7800000       1.44      0.23  0.7800000
## 134   131  0.7800000       1.44      0.23  0.7800000
## 135   131  0.7800000       1.44      0.23  0.7800000
## 136   131  0.7800000       1.44      0.23  0.7800000
## 137   131  0.7800000       1.44      0.23  0.7800000
## 138   131  0.7800000       1.44      0.23  0.7800000
## 139   131  0.7800000       1.44      0.23  0.7800000
## 140   131  0.7800000       1.44      0.23  0.7800000
## 141   131  0.7800000       1.44      0.23  0.7800000
## 142   131  0.7800000       1.44      0.23  0.7800000
## 143   131  0.7800000       1.44      0.23  0.7800000
## 144   132 49.0200000      48.99     46.17 49.0200000
## 145   132 49.0200000      48.99     46.17 49.0200000
## 146   132 49.0200000      48.99     46.17 49.0200000
## 147   132 49.0200000      48.99     46.17 49.0200000
## 148   132 49.0200000      48.99     46.17 49.0200000
## 149   132 49.0200000      48.99     46.17 49.0200000
## 150   132 49.0200000      48.99     46.17 49.0200000
## 151   132 49.0200000      48.99     46.17 49.0200000
## 152   132 49.0200000      48.99     46.17 49.0200000
## 153   132 49.0200000      48.99     46.17 49.0200000
## 154   132 49.0200000      48.99     46.17 49.0200000
## 155   132 49.0200000      48.99     46.17 49.0200000
## 156   132 49.0200000      48.99     46.17 49.0200000
## 157   133  2.3300000       3.64      1.46  2.3300000
## 158   133  2.3300000       3.64      1.46  2.3300000
## 159   133  2.3300000       3.64      1.46  2.3300000
## 160   133  2.3300000       3.64      1.46  2.3300000
## 161   133  2.3300000       3.64      1.46  2.3300000
## 162   133  2.3300000       3.64      1.46  2.3300000
## 163   133  2.3300000       3.64      1.46  2.3300000
## 164   133  2.3300000       3.64      1.46  2.3300000
## 165   133  2.3300000       3.64      1.46  2.3300000
## 166   133  2.3300000       3.64      1.46  2.3300000
## 167   133  2.3300000       3.64      1.46  2.3300000
## 168   133  2.3300000       3.64      1.46  2.3300000
## 169   133  2.3300000       3.64      1.46  2.3300000
## 170   135  6.8600000       6.36      6.07  6.8600000
## 171   135  6.8600000       6.36      6.07  6.8600000
## 172   135  6.8600000       6.36      6.07  6.8600000
## 173   135  6.8600000       6.36      6.07  6.8600000
## 174   135  6.8600000       6.36      6.07  6.8600000
## 175   135  6.8600000       6.36      6.07  6.8600000
## 176   135  6.8600000       6.36      6.07  6.8600000
## 177   135  6.8600000       6.36      6.07  6.8600000
## 178   135  6.8600000       6.36      6.07  6.8600000
## 179   135  6.8600000       6.36      6.07  6.8600000
## 180   135  6.8600000       6.36      6.07  6.8600000
## 181   135  6.8600000       6.36      6.07  6.8600000
## 182   135  6.8600000       6.36      6.07  6.8600000
## 183   136  4.4900000       5.98      4.42  4.4900000
## 184   136  4.4900000       5.98      4.42  4.4900000
## 185   136  4.4900000       5.98      4.42  4.4900000
## 186   136  4.4900000       5.98      4.42  4.4900000
## 187   136  4.4900000       5.98      4.42  4.4900000
## 188   136  4.4900000       5.98      4.42  4.4900000
## 189   136  4.4900000       5.98      4.42  4.4900000
## 190   136  4.4900000       5.98      4.42  4.4900000
## 191   136  4.4900000       5.98      4.42  4.4900000
## 192   136  4.4900000       5.98      4.42  4.4900000
## 193   136  4.4900000       5.98      4.42  4.4900000
## 194   136  4.4900000       5.98      4.42  4.4900000
## 195   136  4.4900000       5.98      4.42  4.4900000
## 196   137  8.4500000       9.87      9.57  8.4500000
## 197   137  8.4500000       9.87      9.57  8.4500000
## 198   137  8.4500000       9.87      9.57  8.4500000
## 199   137  8.4500000       9.87      9.57  8.4500000
## 200   137  8.4500000       9.87      9.57  8.4500000
## 201   137  8.4500000       9.87      9.57  8.4500000
## 202   137  8.4500000       9.87      9.57  8.4500000
## 203   137  8.4500000       9.87      9.57  8.4500000
## 204   137  8.4500000       9.87      9.57  8.4500000
## 205   137  8.4500000       9.87      9.57  8.4500000
## 206   137  8.4500000       9.87      9.57  8.4500000
## 207   137  8.4500000       9.87      9.57  8.4500000
## 208   137  8.4500000       9.87      9.57  8.4500000
## 209   138 28.5500000      28.52     29.42 28.5500000
## 210   138 28.5500000      28.52     29.42 28.5500000
## 211   138 28.5500000      28.52     29.42 28.5500000
## 212   138 28.5500000      28.52     29.42 28.5500000
## 213   138 28.5500000      28.52     29.42 28.5500000
## 214   138 28.5500000      28.52     29.42 28.5500000
## 215   138 28.5500000      28.52     29.42 28.5500000
## 216   138 28.5500000      28.52     29.42 28.5500000
## 217   138 28.5500000      28.52     29.42 28.5500000
## 218   138 28.5500000      28.52     29.42 28.5500000
## 219   138 28.5500000      28.52     29.42 28.5500000
## 220   138 28.5500000      28.52     29.42 28.5500000
## 221   138 28.5500000      28.52     29.42 28.5500000
## 222   140  6.5700000       7.86     10.03  6.5700000
## 223   140  6.5700000       7.86     10.03  6.5700000
## 224   140  6.5700000       7.86     10.03  6.5700000
## 225   140  6.5700000       7.86     10.03  6.5700000
## 226   140  6.5700000       7.86     10.03  6.5700000
## 227   140  6.5700000       7.86     10.03  6.5700000
## 228   140  6.5700000       7.86     10.03  6.5700000
## 229   140  6.5700000       7.86     10.03  6.5700000
## 230   140  6.5700000       7.86     10.03  6.5700000
## 231   140  6.5700000       7.86     10.03  6.5700000
## 232   140  6.5700000       7.86     10.03  6.5700000
## 233   140  6.5700000       7.86     10.03  6.5700000
## 234   140  6.5700000       7.86     10.03  6.5700000
## 235   143 34.2900000      35.06     34.95 34.2900000
## 236   143 34.2900000      35.06     34.95 34.2900000
## 237   143 34.2900000      35.06     34.95 34.2900000
## 238   143 34.2900000      35.06     34.95 34.2900000
## 239   143 34.2900000      35.06     34.95 34.2900000
## 240   143 34.2900000      35.06     34.95 34.2900000
## 241   143 34.2900000      35.06     34.95 34.2900000
## 242   143 34.2900000      35.06     34.95 34.2900000
## 243   143 34.2900000      35.06     34.95 34.2900000
## 244   143 34.2900000      35.06     34.95 34.2900000
## 245   143 34.2900000      35.06     34.95 34.2900000
## 246   143 34.2900000      35.06     34.95 34.2900000
## 247   143 34.2900000      35.06     34.95 34.2900000
## 248   144 41.1900000      42.23     43.46 41.1900000
## 249   144 41.1900000      42.23     43.46 41.1900000
## 250   144 41.1900000      42.23     43.46 41.1900000
## 251   144 41.1900000      42.23     43.46 41.1900000
## 252   144 41.1900000      42.23     43.46 41.1900000
## 253   144 41.1900000      42.23     43.46 41.1900000
## 254   144 41.1900000      42.23     43.46 41.1900000
## 255   144 41.1900000      42.23     43.46 41.1900000
## 256   144 41.1900000      42.23     43.46 41.1900000
## 257   144 41.1900000      42.23     43.46 41.1900000
## 258   144 41.1900000      42.23     43.46 41.1900000
## 259   144 41.1900000      42.23     43.46 41.1900000
## 260   144 41.1900000      42.23     43.46 41.1900000
## 261   145  0.6300000       2.72      1.06  0.6300000
## 262   145  0.6300000       2.72      1.06  0.6300000
## 263   145  0.6300000       2.72      1.06  0.6300000
## 264   145  0.6300000       2.72      1.06  0.6300000
## 265   145  0.6300000       2.72      1.06  0.6300000
## 266   145  0.6300000       2.72      1.06  0.6300000
## 267   145  0.6300000       2.72      1.06  0.6300000
## 268   145  0.6300000       2.72      1.06  0.6300000
## 269   145  0.6300000       2.72      1.06  0.6300000
## 270   145  0.6300000       2.72      1.06  0.6300000
## 271   145  0.6300000       2.72      1.06  0.6300000
## 272   145  0.6300000       2.72      1.06  0.6300000
## 273   145  0.6300000       2.72      1.06  0.6300000
## 274   147 27.7000000      26.94     24.98 27.7000000
## 275   147 27.7000000      26.94     24.98 27.7000000
## 276   147 27.7000000      26.94     24.98 27.7000000
## 277   147 27.7000000      26.94     24.98 27.7000000
## 278   147 27.7000000      26.94     24.98 27.7000000
## 279   147 27.7000000      26.94     24.98 27.7000000
## 280   147 27.7000000      26.94     24.98 27.7000000
## 281   147 27.7000000      26.94     24.98 27.7000000
## 282   147 27.7000000      26.94     24.98 27.7000000
## 283   147 27.7000000      26.94     24.98 27.7000000
## 284   147 27.7000000      26.94     24.98 27.7000000
## 285   147 27.7000000      26.94     24.98 27.7000000
## 286   147 27.7000000      26.94     24.98 27.7000000
## 287   149 13.1600000      14.42     10.16 13.1600000
## 288   149 13.1600000      14.42     10.16 13.1600000
## 289   149 13.1600000      14.42     10.16 13.1600000
## 290   149 13.1600000      14.42     10.16 13.1600000
## 291   149 13.1600000      14.42     10.16 13.1600000
## 292   149 13.1600000      14.42     10.16 13.1600000
## 293   149 13.1600000      14.42     10.16 13.1600000
## 294   149 13.1600000      14.42     10.16 13.1600000
## 295   149 13.1600000      14.42     10.16 13.1600000
## 296   149 13.1600000      14.42     10.16 13.1600000
## 297   149 13.1600000      14.42     10.16 13.1600000
## 298   149 13.1600000      14.42     10.16 13.1600000
## 299   149 13.1600000      14.42     10.16 13.1600000
## 300    15 57.5300000      55.76     60.20 57.5300000
## 301    15 57.5300000      55.76     60.20 57.5300000
## 302    15 57.5300000      55.76     60.20 57.5300000
## 303    15 57.5300000      55.76     60.20 57.5300000
## 304    15 57.5300000      55.76     60.20 57.5300000
## 305    15 57.5300000      55.76     60.20 57.5300000
## 306    15 57.5300000      55.76     60.20 57.5300000
## 307    15 57.5300000      55.76     60.20 57.5300000
## 308    15 57.5300000      55.76     60.20 57.5300000
## 309    15 57.5300000      55.76     60.20 57.5300000
## 310    15 57.5300000      55.76     60.20 57.5300000
## 311    15 57.5300000      55.76     60.20 57.5300000
## 312    15 57.5300000      55.76     60.20 57.5300000
## 313   152  9.6600000      10.89     12.44  9.6600000
## 314   152  9.6600000      10.89     12.44  9.6600000
## 315   152  9.6600000      10.89     12.44  9.6600000
## 316   152  9.6600000      10.89     12.44  9.6600000
## 317   152  9.6600000      10.89     12.44  9.6600000
## 318   152  9.6600000      10.89     12.44  9.6600000
## 319   152  9.6600000      10.89     12.44  9.6600000
## 320   152  9.6600000      10.89     12.44  9.6600000
## 321   152  9.6600000      10.89     12.44  9.6600000
## 322   152  9.6600000      10.89     12.44  9.6600000
## 323   152  9.6600000      10.89     12.44  9.6600000
## 324   152  9.6600000      10.89     12.44  9.6600000
## 325   152  9.6600000      10.89     12.44  9.6600000
## 326   153  8.5000000       9.12      6.99  8.5000000
## 327   153  8.5000000       9.12      6.99  8.5000000
## 328   153  8.5000000       9.12      6.99  8.5000000
## 329   153  8.5000000       9.12      6.99  8.5000000
## 330   153  8.5000000       9.12      6.99  8.5000000
## 331   153  8.5000000       9.12      6.99  8.5000000
## 332   153  8.5000000       9.12      6.99  8.5000000
## 333   153  8.5000000       9.12      6.99  8.5000000
## 334   153  8.5000000       9.12      6.99  8.5000000
## 335   153  8.5000000       9.12      6.99  8.5000000
## 336   153  8.5000000       9.12      6.99  8.5000000
## 337   153  8.5000000       9.12      6.99  8.5000000
## 338   153  8.5000000       9.12      6.99  8.5000000
## 339   157 15.0300000      15.70     15.77 15.0300000
## 340   157 15.0300000      15.70     15.77 15.0300000
## 341   157 15.0300000      15.70     15.77 15.0300000
## 342   157 15.0300000      15.70     15.77 15.0300000
## 343   157 15.0300000      15.70     15.77 15.0300000
## 344   157 15.0300000      15.70     15.77 15.0300000
## 345   157 15.0300000      15.70     15.77 15.0300000
## 346   157 15.0300000      15.70     15.77 15.0300000
## 347   157 15.0300000      15.70     15.77 15.0300000
## 348   157 15.0300000      15.70     15.77 15.0300000
## 349   157 15.0300000      15.70     15.77 15.0300000
## 350   157 15.0300000      15.70     15.77 15.0300000
## 351   157 15.0300000      15.70     15.77 15.0300000
## 352   158 13.8900000      14.89     10.71 13.8900000
## 353   158 13.8900000      14.89     10.71 13.8900000
## 354   158 13.8900000      14.89     10.71 13.8900000
## 355   158 13.8900000      14.89     10.71 13.8900000
## 356   158 13.8900000      14.89     10.71 13.8900000
## 357   158 13.8900000      14.89     10.71 13.8900000
## 358   158 13.8900000      14.89     10.71 13.8900000
## 359   158 13.8900000      14.89     10.71 13.8900000
## 360   158 13.8900000      14.89     10.71 13.8900000
## 361   158 13.8900000      14.89     10.71 13.8900000
## 362   158 13.8900000      14.89     10.71 13.8900000
## 363   158 13.8900000      14.89     10.71 13.8900000
## 364   158 13.8900000      14.89     10.71 13.8900000
## 365   159 10.9200000      12.46      7.19 10.9200000
## 366   159 10.9200000      12.46      7.19 10.9200000
## 367   159 10.9200000      12.46      7.19 10.9200000
## 368   159 10.9200000      12.46      7.19 10.9200000
## 369   159 10.9200000      12.46      7.19 10.9200000
## 370   159 10.9200000      12.46      7.19 10.9200000
## 371   159 10.9200000      12.46      7.19 10.9200000
## 372   159 10.9200000      12.46      7.19 10.9200000
## 373   159 10.9200000      12.46      7.19 10.9200000
## 374   159 10.9200000      12.46      7.19 10.9200000
## 375   159 10.9200000      12.46      7.19 10.9200000
## 376   159 10.9200000      12.46      7.19 10.9200000
## 377   159 10.9200000      12.46      7.19 10.9200000
## 378    16 34.5000000      33.33     33.64 34.5000000
## 379    16 34.5000000      33.33     33.64 34.5000000
## 380    16 34.5000000      33.33     33.64 34.5000000
## 381    16 34.5000000      33.33     33.64 34.5000000
## 382    16 34.5000000      33.33     33.64 34.5000000
## 383    16 34.5000000      33.33     33.64 34.5000000
## 384    16 34.5000000      33.33     33.64 34.5000000
## 385    16 34.5000000      33.33     33.64 34.5000000
## 386    16 34.5000000      33.33     33.64 34.5000000
## 387    16 34.5000000      33.33     33.64 34.5000000
## 388    16 34.5000000      33.33     33.64 34.5000000
## 389    16 34.5000000      33.33     33.64 34.5000000
## 390    16 34.5000000      33.33     33.64 34.5000000
## 391   160  9.5700000      10.15      7.92  9.5700000
## 392   160  9.5700000      10.15      7.92  9.5700000
## 393   160  9.5700000      10.15      7.92  9.5700000
## 394   160  9.5700000      10.15      7.92  9.5700000
## 395   160  9.5700000      10.15      7.92  9.5700000
## 396   160  9.5700000      10.15      7.92  9.5700000
## 397   160  9.5700000      10.15      7.92  9.5700000
## 398   160  9.5700000      10.15      7.92  9.5700000
## 399   160  9.5700000      10.15      7.92  9.5700000
## 400   160  9.5700000      10.15      7.92  9.5700000
## 401   160  9.5700000      10.15      7.92  9.5700000
## 402   160  9.5700000      10.15      7.92  9.5700000
## 403   160  9.5700000      10.15      7.92  9.5700000
## 404   161  4.5600000       5.12      3.24  4.5600000
## 405   161  4.5600000       5.12      3.24  4.5600000
## 406   161  4.5600000       5.12      3.24  4.5600000
## 407   161  4.5600000       5.12      3.24  4.5600000
## 408   161  4.5600000       5.12      3.24  4.5600000
## 409   161  4.5600000       5.12      3.24  4.5600000
## 410   161  4.5600000       5.12      3.24  4.5600000
## 411   161  4.5600000       5.12      3.24  4.5600000
## 412   161  4.5600000       5.12      3.24  4.5600000
## 413   161  4.5600000       5.12      3.24  4.5600000
## 414   161  4.5600000       5.12      3.24  4.5600000
## 415   161  4.5600000       5.12      3.24  4.5600000
## 416   161  4.5600000       5.12      3.24  4.5600000
## 417   162 48.9600000      50.33     51.06 48.9600000
## 418   162 48.9600000      50.33     51.06 48.9600000
## 419   162 48.9600000      50.33     51.06 48.9600000
## 420   162 48.9600000      50.33     51.06 48.9600000
## 421   162 48.9600000      50.33     51.06 48.9600000
## 422   162 48.9600000      50.33     51.06 48.9600000
## 423   162 48.9600000      50.33     51.06 48.9600000
## 424   162 48.9600000      50.33     51.06 48.9600000
## 425   162 48.9600000      50.33     51.06 48.9600000
## 426   162 48.9600000      50.33     51.06 48.9600000
## 427   162 48.9600000      50.33     51.06 48.9600000
## 428   162 48.9600000      50.33     51.06 48.9600000
## 429   162 48.9600000      50.33     51.06 48.9600000
## 430   163  3.0300000       4.14      2.15  3.0300000
## 431   163  3.0300000       4.14      2.15  3.0300000
## 432   163  3.0300000       4.14      2.15  3.0300000
## 433   163  3.0300000       4.14      2.15  3.0300000
## 434   163  3.0300000       4.14      2.15  3.0300000
## 435   163  3.0300000       4.14      2.15  3.0300000
## 436   163  3.0300000       4.14      2.15  3.0300000
## 437   163  3.0300000       4.14      2.15  3.0300000
## 438   163  3.0300000       4.14      2.15  3.0300000
## 439   163  3.0300000       4.14      2.15  3.0300000
## 440   163  3.0300000       4.14      2.15  3.0300000
## 441   163  3.0300000       4.14      2.15  3.0300000
## 442   163  3.0300000       4.14      2.15  3.0300000
## 443   164 20.3200000      19.61     22.22 20.3200000
## 444   164 20.3200000      19.61     22.22 20.3200000
## 445   164 20.3200000      19.61     22.22 20.3200000
## 446   164 20.3200000      19.61     22.22 20.3200000
## 447   164 20.3200000      19.61     22.22 20.3200000
## 448   164 20.3200000      19.61     22.22 20.3200000
## 449   164 20.3200000      19.61     22.22 20.3200000
## 450   164 20.3200000      19.61     22.22 20.3200000
## 451   164 20.3200000      19.61     22.22 20.3200000
## 452   164 20.3200000      19.61     22.22 20.3200000
## 453   164 20.3200000      19.61     22.22 20.3200000
## 454   164 20.3200000      19.61     22.22 20.3200000
## 455   164 20.3200000      19.61     22.22 20.3200000
## 456   165 25.7400000      25.03     30.63 25.7400000
## 457   165 25.7400000      25.03     30.63 25.7400000
## 458   165 25.7400000      25.03     30.63 25.7400000
## 459   165 25.7400000      25.03     30.63 25.7400000
## 460   165 25.7400000      25.03     30.63 25.7400000
## 461   165 25.7400000      25.03     30.63 25.7400000
## 462   165 25.7400000      25.03     30.63 25.7400000
## 463   165 25.7400000      25.03     30.63 25.7400000
## 464   165 25.7400000      25.03     30.63 25.7400000
## 465   165 25.7400000      25.03     30.63 25.7400000
## 466   165 25.7400000      25.03     30.63 25.7400000
## 467   165 25.7400000      25.03     30.63 25.7400000
## 468   165 25.7400000      25.03     30.63 25.7400000
## 469   166  2.4100000       3.50      3.84  2.4100000
## 470   166  2.4100000       3.50      3.84  2.4100000
## 471   166  2.4100000       3.50      3.84  2.4100000
## 472   166  2.4100000       3.50      3.84  2.4100000
## 473   166  2.4100000       3.50      3.84  2.4100000
## 474   166  2.4100000       3.50      3.84  2.4100000
## 475   166  2.4100000       3.50      3.84  2.4100000
## 476   166  2.4100000       3.50      3.84  2.4100000
## 477   166  2.4100000       3.50      3.84  2.4100000
## 478   166  2.4100000       3.50      3.84  2.4100000
## 479   166  2.4100000       3.50      3.84  2.4100000
## 480   166  2.4100000       3.50      3.84  2.4100000
## 481   166  2.4100000       3.50      3.84  2.4100000
## 482   167  2.7000000       3.77      1.78  2.7000000
## 483   167  2.7000000       3.77      1.78  2.7000000
## 484   167  2.7000000       3.77      1.78  2.7000000
## 485   167  2.7000000       3.77      1.78  2.7000000
## 486   167  2.7000000       3.77      1.78  2.7000000
## 487   167  2.7000000       3.77      1.78  2.7000000
## 488   167  2.7000000       3.77      1.78  2.7000000
## 489   167  2.7000000       3.77      1.78  2.7000000
## 490   167  2.7000000       3.77      1.78  2.7000000
## 491   167  2.7000000       3.77      1.78  2.7000000
## 492   167  2.7000000       3.77      1.78  2.7000000
## 493   167  2.7000000       3.77      1.78  2.7000000
## 494   167  2.7000000       3.77      1.78  2.7000000
## 495   168 52.8000000      51.61     51.46 52.8000000
## 496   168 52.8000000      51.61     51.46 52.8000000
## 497   168 52.8000000      51.61     51.46 52.8000000
## 498   168 52.8000000      51.61     51.46 52.8000000
## 499   168 52.8000000      51.61     51.46 52.8000000
## 500   168 52.8000000      51.61     51.46 52.8000000
## 501   168 52.8000000      51.61     51.46 52.8000000
## 502   168 52.8000000      51.61     51.46 52.8000000
## 503   168 52.8000000      51.61     51.46 52.8000000
## 504   168 52.8000000      51.61     51.46 52.8000000
## 505   168 52.8000000      51.61     51.46 52.8000000
## 506   168 52.8000000      51.61     51.46 52.8000000
## 507   168 52.8000000      51.61     51.46 52.8000000
## 508   169 21.9800000      22.04     25.33 21.9800000
## 509   169 21.9800000      22.04     25.33 21.9800000
## 510   169 21.9800000      22.04     25.33 21.9800000
## 511   169 21.9800000      22.04     25.33 21.9800000
## 512   169 21.9800000      22.04     25.33 21.9800000
## 513   169 21.9800000      22.04     25.33 21.9800000
## 514   169 21.9800000      22.04     25.33 21.9800000
## 515   169 21.9800000      22.04     25.33 21.9800000
## 516   169 21.9800000      22.04     25.33 21.9800000
## 517   169 21.9800000      22.04     25.33 21.9800000
## 518   169 21.9800000      22.04     25.33 21.9800000
## 519   169 21.9800000      22.04     25.33 21.9800000
## 520   169 21.9800000      22.04     25.33 21.9800000
## 521    17 25.4100000      24.36     27.97 25.4100000
## 522    17 25.4100000      24.36     27.97 25.4100000
## 523    17 25.4100000      24.36     27.97 25.4100000
## 524    17 25.4100000      24.36     27.97 25.4100000
## 525    17 25.4100000      24.36     27.97 25.4100000
## 526    17 25.4100000      24.36     27.97 25.4100000
## 527    17 25.4100000      24.36     27.97 25.4100000
## 528    17 25.4100000      24.36     27.97 25.4100000
## 529    17 25.4100000      24.36     27.97 25.4100000
## 530    17 25.4100000      24.36     27.97 25.4100000
## 531    17 25.4100000      24.36     27.97 25.4100000
## 532    17 25.4100000      24.36     27.97 25.4100000
## 533    17 25.4100000      24.36     27.97 25.4100000
## 534   175 25.6400000      26.41     27.21 25.6400000
## 535   175 25.6400000      26.41     27.21 25.6400000
## 536   175 25.6400000      26.41     27.21 25.6400000
## 537   175 25.6400000      26.41     27.21 25.6400000
## 538   175 25.6400000      26.41     27.21 25.6400000
## 539   175 25.6400000      26.41     27.21 25.6400000
## 540   175 25.6400000      26.41     27.21 25.6400000
## 541   175 25.6400000      26.41     27.21 25.6400000
## 542   175 25.6400000      26.41     27.21 25.6400000
## 543   175 25.6400000      26.41     27.21 25.6400000
## 544   175 25.6400000      26.41     27.21 25.6400000
## 545   175 25.6400000      26.41     27.21 25.6400000
## 546   175 25.6400000      26.41     27.21 25.6400000
## 547   177  0.9371734       1.14      2.71  0.9371734
## 548   177  0.9371734       1.14      2.71  0.9371734
## 549   177  0.9371734       1.14      2.71  0.9371734
## 550   177  0.9371734       1.14      2.71  0.9371734
## 551   177  0.9371734       1.14      2.71  0.9371734
## 552   177  0.9371734       1.14      2.71  0.9371734
## 553   177  0.9371734       1.14      2.71  0.9371734
## 554   177  0.9371734       1.14      2.71  0.9371734
## 555   177  0.9371734       1.14      2.71  0.9371734
## 556   177  0.9371734       1.14      2.71  0.9371734
## 557   177  0.9371734       1.14      2.71  0.9371734
## 558   177  0.9371734       1.14      2.71  0.9371734
## 559   177  0.9371734       1.14      2.71  0.9371734
## 560    18 31.8300000      32.84     32.81 31.8300000
## 561    18 31.8300000      32.84     32.81 31.8300000
## 562    18 31.8300000      32.84     32.81 31.8300000
## 563    18 31.8300000      32.84     32.81 31.8300000
## 564    18 31.8300000      32.84     32.81 31.8300000
## 565    18 31.8300000      32.84     32.81 31.8300000
## 566    18 31.8300000      32.84     32.81 31.8300000
## 567    18 31.8300000      32.84     32.81 31.8300000
## 568    18 31.8300000      32.84     32.81 31.8300000
## 569    18 31.8300000      32.84     32.81 31.8300000
## 570    18 31.8300000      32.84     32.81 31.8300000
## 571    18 31.8300000      32.84     32.81 31.8300000
## 572    18 31.8300000      32.84     32.81 31.8300000
## 573    19 15.8700000      14.65     18.41 15.8700000
## 574    19 15.8700000      14.65     18.41 15.8700000
## 575    19 15.8700000      14.65     18.41 15.8700000
## 576    19 15.8700000      14.65     18.41 15.8700000
## 577    19 15.8700000      14.65     18.41 15.8700000
## 578    19 15.8700000      14.65     18.41 15.8700000
## 579    19 15.8700000      14.65     18.41 15.8700000
## 580    19 15.8700000      14.65     18.41 15.8700000
## 581    19 15.8700000      14.65     18.41 15.8700000
## 582    19 15.8700000      14.65     18.41 15.8700000
## 583    19 15.8700000      14.65     18.41 15.8700000
## 584    19 15.8700000      14.65     18.41 15.8700000
## 585    19 15.8700000      14.65     18.41 15.8700000
## 586     2 15.5300000      16.25     15.17 15.5300000
## 587     2 15.5300000      16.25     15.17 15.5300000
## 588     2 15.5300000      16.25     15.17 15.5300000
## 589     2 15.5300000      16.25     15.17 15.5300000
## 590     2 15.5300000      16.25     15.17 15.5300000
## 591     2 15.5300000      16.25     15.17 15.5300000
## 592     2 15.5300000      16.25     15.17 15.5300000
## 593     2 15.5300000      16.25     15.17 15.5300000
## 594     2 15.5300000      16.25     15.17 15.5300000
## 595     2 15.5300000      16.25     15.17 15.5300000
## 596     2 15.5300000      16.25     15.17 15.5300000
## 597     2 15.5300000      16.25     15.17 15.5300000
## 598     2 15.5300000      16.25     15.17 15.5300000
## 599    20 32.0400000      31.99     32.48 32.0400000
## 600    20 32.0400000      31.99     32.48 32.0400000
## 601    20 32.0400000      31.99     32.48 32.0400000
## 602    20 32.0400000      31.99     32.48 32.0400000
## 603    20 32.0400000      31.99     32.48 32.0400000
## 604    20 32.0400000      31.99     32.48 32.0400000
## 605    20 32.0400000      31.99     32.48 32.0400000
## 606    20 32.0400000      31.99     32.48 32.0400000
## 607    20 32.0400000      31.99     32.48 32.0400000
## 608    20 32.0400000      31.99     32.48 32.0400000
## 609    20 32.0400000      31.99     32.48 32.0400000
## 610    20 32.0400000      31.99     32.48 32.0400000
## 611    20 32.0400000      31.99     32.48 32.0400000
## 612    21 45.2000000      45.46     45.68 45.2000000
## 613    21 45.2000000      45.46     45.68 45.2000000
## 614    21 45.2000000      45.46     45.68 45.2000000
## 615    21 45.2000000      45.46     45.68 45.2000000
## 616    21 45.2000000      45.46     45.68 45.2000000
## 617    21 45.2000000      45.46     45.68 45.2000000
## 618    21 45.2000000      45.46     45.68 45.2000000
## 619    21 45.2000000      45.46     45.68 45.2000000
## 620    21 45.2000000      45.46     45.68 45.2000000
## 621    21 45.2000000      45.46     45.68 45.2000000
## 622    21 45.2000000      45.46     45.68 45.2000000
## 623    21 45.2000000      45.46     45.68 45.2000000
## 624    21 45.2000000      45.46     45.68 45.2000000
## 625    22 58.5600000      57.95     63.42 58.5600000
## 626    22 58.5600000      57.95     63.42 58.5600000
## 627    22 58.5600000      57.95     63.42 58.5600000
## 628    22 58.5600000      57.95     63.42 58.5600000
## 629    22 58.5600000      57.95     63.42 58.5600000
## 630    22 58.5600000      57.95     63.42 58.5600000
## 631    22 58.5600000      57.95     63.42 58.5600000
## 632    22 58.5600000      57.95     63.42 58.5600000
## 633    22 58.5600000      57.95     63.42 58.5600000
## 634    22 58.5600000      57.95     63.42 58.5600000
## 635    22 58.5600000      57.95     63.42 58.5600000
## 636    22 58.5600000      57.95     63.42 58.5600000
## 637    22 58.5600000      57.95     63.42 58.5600000
## 638    26  2.9600000       3.85      3.04  2.9600000
## 639    26  2.9600000       3.85      3.04  2.9600000
## 640    26  2.9600000       3.85      3.04  2.9600000
## 641    26  2.9600000       3.85      3.04  2.9600000
## 642    26  2.9600000       3.85      3.04  2.9600000
## 643    26  2.9600000       3.85      3.04  2.9600000
## 644    26  2.9600000       3.85      3.04  2.9600000
## 645    26  2.9600000       3.85      3.04  2.9600000
## 646    26  2.9600000       3.85      3.04  2.9600000
## 647    26  2.9600000       3.85      3.04  2.9600000
## 648    26  2.9600000       3.85      3.04  2.9600000
## 649    26  2.9600000       3.85      3.04  2.9600000
## 650    26  2.9600000       3.85      3.04  2.9600000
## 651    29  1.8900000       2.91      0.90  1.8900000
## 652    29  1.8900000       2.91      0.90  1.8900000
## 653    29  1.8900000       2.91      0.90  1.8900000
## 654    29  1.8900000       2.91      0.90  1.8900000
## 655    29  1.8900000       2.91      0.90  1.8900000
## 656    29  1.8900000       2.91      0.90  1.8900000
## 657    29  1.8900000       2.91      0.90  1.8900000
## 658    29  1.8900000       2.91      0.90  1.8900000
## 659    29  1.8900000       2.91      0.90  1.8900000
## 660    29  1.8900000       2.91      0.90  1.8900000
## 661    29  1.8900000       2.91      0.90  1.8900000
## 662    29  1.8900000       2.91      0.90  1.8900000
## 663    29  1.8900000       2.91      0.90  1.8900000
## 664     3  8.3800000       9.42      9.71  8.3800000
## 665     3  8.3800000       9.42      9.71  8.3800000
## 666     3  8.3800000       9.42      9.71  8.3800000
## 667     3  8.3800000       9.42      9.71  8.3800000
## 668     3  8.3800000       9.42      9.71  8.3800000
## 669     3  8.3800000       9.42      9.71  8.3800000
## 670     3  8.3800000       9.42      9.71  8.3800000
## 671     3  8.3800000       9.42      9.71  8.3800000
## 672     3  8.3800000       9.42      9.71  8.3800000
## 673     3  8.3800000       9.42      9.71  8.3800000
## 674     3  8.3800000       9.42      9.71  8.3800000
## 675     3  8.3800000       9.42      9.71  8.3800000
## 676     3  8.3800000       9.42      9.71  8.3800000
## 677    31 14.8500000      15.52     15.34 14.8500000
## 678    31 14.8500000      15.52     15.34 14.8500000
## 679    31 14.8500000      15.52     15.34 14.8500000
## 680    31 14.8500000      15.52     15.34 14.8500000
## 681    31 14.8500000      15.52     15.34 14.8500000
## 682    31 14.8500000      15.52     15.34 14.8500000
## 683    31 14.8500000      15.52     15.34 14.8500000
## 684    31 14.8500000      15.52     15.34 14.8500000
## 685    31 14.8500000      15.52     15.34 14.8500000
## 686    31 14.8500000      15.52     15.34 14.8500000
## 687    31 14.8500000      15.52     15.34 14.8500000
## 688    31 14.8500000      15.52     15.34 14.8500000
## 689    31 14.8500000      15.52     15.34 14.8500000
## 690    32  2.5100000       3.10      2.85  2.5100000
## 691    32  2.5100000       3.10      2.85  2.5100000
## 692    32  2.5100000       3.10      2.85  2.5100000
## 693    32  2.5100000       3.10      2.85  2.5100000
## 694    32  2.5100000       3.10      2.85  2.5100000
## 695    32  2.5100000       3.10      2.85  2.5100000
## 696    32  2.5100000       3.10      2.85  2.5100000
## 697    32  2.5100000       3.10      2.85  2.5100000
## 698    32  2.5100000       3.10      2.85  2.5100000
## 699    32  2.5100000       3.10      2.85  2.5100000
## 700    32  2.5100000       3.10      2.85  2.5100000
## 701    32  2.5100000       3.10      2.85  2.5100000
## 702    32  2.5100000       3.10      2.85  2.5100000
## 703    34 47.2900000      49.72     47.24 47.2900000
## 704    34 47.2900000      49.72     47.24 47.2900000
## 705    34 47.2900000      49.72     47.24 47.2900000
## 706    34 47.2900000      49.72     47.24 47.2900000
## 707    34 47.2900000      49.72     47.24 47.2900000
## 708    34 47.2900000      49.72     47.24 47.2900000
## 709    34 47.2900000      49.72     47.24 47.2900000
## 710    34 47.2900000      49.72     47.24 47.2900000
## 711    34 47.2900000      49.72     47.24 47.2900000
## 712    34 47.2900000      49.72     47.24 47.2900000
## 713    34 47.2900000      49.72     47.24 47.2900000
## 714    34 47.2900000      49.72     47.24 47.2900000
## 715    34 47.2900000      49.72     47.24 47.2900000
## 716    35  0.4200000       1.71      0.54  0.4200000
## 717    35  0.4200000       1.71      0.54  0.4200000
## 718    35  0.4200000       1.71      0.54  0.4200000
## 719    35  0.4200000       1.71      0.54  0.4200000
## 720    35  0.4200000       1.71      0.54  0.4200000
## 721    35  0.4200000       1.71      0.54  0.4200000
## 722    35  0.4200000       1.71      0.54  0.4200000
## 723    35  0.4200000       1.71      0.54  0.4200000
## 724    35  0.4200000       1.71      0.54  0.4200000
## 725    35  0.4200000       1.71      0.54  0.4200000
## 726    35  0.4200000       1.71      0.54  0.4200000
## 727    35  0.4200000       1.71      0.54  0.4200000
## 728    35  0.4200000       1.71      0.54  0.4200000
## 729    36 33.2500000      33.17     33.98 33.2500000
## 730    36 33.2500000      33.17     33.98 33.2500000
## 731    36 33.2500000      33.17     33.98 33.2500000
## 732    36 33.2500000      33.17     33.98 33.2500000
## 733    36 33.2500000      33.17     33.98 33.2500000
## 734    36 33.2500000      33.17     33.98 33.2500000
## 735    36 33.2500000      33.17     33.98 33.2500000
## 736    36 33.2500000      33.17     33.98 33.2500000
## 737    36 33.2500000      33.17     33.98 33.2500000
## 738    36 33.2500000      33.17     33.98 33.2500000
## 739    36 33.2500000      33.17     33.98 33.2500000
## 740    36 33.2500000      33.17     33.98 33.2500000
## 741    36 33.2500000      33.17     33.98 33.2500000
## 742    37 19.0700000      18.60     21.20 19.0700000
## 743    37 19.0700000      18.60     21.20 19.0700000
## 744    37 19.0700000      18.60     21.20 19.0700000
## 745    37 19.0700000      18.60     21.20 19.0700000
## 746    37 19.0700000      18.60     21.20 19.0700000
## 747    37 19.0700000      18.60     21.20 19.0700000
## 748    37 19.0700000      18.60     21.20 19.0700000
## 749    37 19.0700000      18.60     21.20 19.0700000
## 750    37 19.0700000      18.60     21.20 19.0700000
## 751    37 19.0700000      18.60     21.20 19.0700000
## 752    37 19.0700000      18.60     21.20 19.0700000
## 753    37 19.0700000      18.60     21.20 19.0700000
## 754    37 19.0700000      18.60     21.20 19.0700000
## 755    38 35.6300000      35.29     33.94 35.6300000
## 756    38 35.6300000      35.29     33.94 35.6300000
## 757    38 35.6300000      35.29     33.94 35.6300000
## 758    38 35.6300000      35.29     33.94 35.6300000
## 759    38 35.6300000      35.29     33.94 35.6300000
## 760    38 35.6300000      35.29     33.94 35.6300000
## 761    38 35.6300000      35.29     33.94 35.6300000
## 762    38 35.6300000      35.29     33.94 35.6300000
## 763    38 35.6300000      35.29     33.94 35.6300000
## 764    38 35.6300000      35.29     33.94 35.6300000
## 765    38 35.6300000      35.29     33.94 35.6300000
## 766    38 35.6300000      35.29     33.94 35.6300000
## 767    38 35.6300000      35.29     33.94 35.6300000
## 768    39 58.5200000      57.45     60.58 58.5200000
## 769    39 58.5200000      57.45     60.58 58.5200000
## 770    39 58.5200000      57.45     60.58 58.5200000
## 771    39 58.5200000      57.45     60.58 58.5200000
## 772    39 58.5200000      57.45     60.58 58.5200000
## 773    39 58.5200000      57.45     60.58 58.5200000
## 774    39 58.5200000      57.45     60.58 58.5200000
## 775    39 58.5200000      57.45     60.58 58.5200000
## 776    39 58.5200000      57.45     60.58 58.5200000
## 777    39 58.5200000      57.45     60.58 58.5200000
## 778    39 58.5200000      57.45     60.58 58.5200000
## 779    39 58.5200000      57.45     60.58 58.5200000
## 780    39 58.5200000      57.45     60.58 58.5200000
## 781    40 30.1500000      30.37     30.09 30.1500000
## 782    40 30.1500000      30.37     30.09 30.1500000
## 783    40 30.1500000      30.37     30.09 30.1500000
## 784    40 30.1500000      30.37     30.09 30.1500000
## 785    40 30.1500000      30.37     30.09 30.1500000
## 786    40 30.1500000      30.37     30.09 30.1500000
## 787    40 30.1500000      30.37     30.09 30.1500000
## 788    40 30.1500000      30.37     30.09 30.1500000
## 789    40 30.1500000      30.37     30.09 30.1500000
## 790    40 30.1500000      30.37     30.09 30.1500000
## 791    40 30.1500000      30.37     30.09 30.1500000
## 792    40 30.1500000      30.37     30.09 30.1500000
## 793    40 30.1500000      30.37     30.09 30.1500000
## 794    41 18.5900000      19.55     17.65 18.5900000
## 795    41 18.5900000      19.55     17.65 18.5900000
## 796    41 18.5900000      19.55     17.65 18.5900000
## 797    41 18.5900000      19.55     17.65 18.5900000
## 798    41 18.5900000      19.55     17.65 18.5900000
## 799    41 18.5900000      19.55     17.65 18.5900000
## 800    41 18.5900000      19.55     17.65 18.5900000
## 801    41 18.5900000      19.55     17.65 18.5900000
## 802    41 18.5900000      19.55     17.65 18.5900000
## 803    41 18.5900000      19.55     17.65 18.5900000
## 804    41 18.5900000      19.55     17.65 18.5900000
## 805    41 18.5900000      19.55     17.65 18.5900000
## 806    41 18.5900000      19.55     17.65 18.5900000
## 807    42 21.4900000      22.19     21.22 21.4900000
## 808    42 21.4900000      22.19     21.22 21.4900000
## 809    42 21.4900000      22.19     21.22 21.4900000
## 810    42 21.4900000      22.19     21.22 21.4900000
## 811    42 21.4900000      22.19     21.22 21.4900000
## 812    42 21.4900000      22.19     21.22 21.4900000
## 813    42 21.4900000      22.19     21.22 21.4900000
## 814    42 21.4900000      22.19     21.22 21.4900000
## 815    42 21.4900000      22.19     21.22 21.4900000
## 816    42 21.4900000      22.19     21.22 21.4900000
## 817    42 21.4900000      22.19     21.22 21.4900000
## 818    42 21.4900000      22.19     21.22 21.4900000
## 819    42 21.4900000      22.19     21.22 21.4900000
## 820    44 16.1900000      15.29     13.94 16.1900000
## 821    44 16.1900000      15.29     13.94 16.1900000
## 822    44 16.1900000      15.29     13.94 16.1900000
## 823    44 16.1900000      15.29     13.94 16.1900000
## 824    44 16.1900000      15.29     13.94 16.1900000
## 825    44 16.1900000      15.29     13.94 16.1900000
## 826    44 16.1900000      15.29     13.94 16.1900000
## 827    44 16.1900000      15.29     13.94 16.1900000
## 828    44 16.1900000      15.29     13.94 16.1900000
## 829    44 16.1900000      15.29     13.94 16.1900000
## 830    44 16.1900000      15.29     13.94 16.1900000
## 831    44 16.1900000      15.29     13.94 16.1900000
## 832    44 16.1900000      15.29     13.94 16.1900000
## 833    45 41.4600000      41.55     38.56 41.4600000
## 834    45 41.4600000      41.55     38.56 41.4600000
## 835    45 41.4600000      41.55     38.56 41.4600000
## 836    45 41.4600000      41.55     38.56 41.4600000
## 837    45 41.4600000      41.55     38.56 41.4600000
## 838    45 41.4600000      41.55     38.56 41.4600000
## 839    45 41.4600000      41.55     38.56 41.4600000
## 840    45 41.4600000      41.55     38.56 41.4600000
## 841    45 41.4600000      41.55     38.56 41.4600000
## 842    45 41.4600000      41.55     38.56 41.4600000
## 843    45 41.4600000      41.55     38.56 41.4600000
## 844    45 41.4600000      41.55     38.56 41.4600000
## 845    45 41.4600000      41.55     38.56 41.4600000
## 846    46  8.4300000       8.31     11.47  8.4300000
## 847    46  8.4300000       8.31     11.47  8.4300000
## 848    46  8.4300000       8.31     11.47  8.4300000
## 849    46  8.4300000       8.31     11.47  8.4300000
## 850    46  8.4300000       8.31     11.47  8.4300000
## 851    46  8.4300000       8.31     11.47  8.4300000
## 852    46  8.4300000       8.31     11.47  8.4300000
## 853    46  8.4300000       8.31     11.47  8.4300000
## 854    46  8.4300000       8.31     11.47  8.4300000
## 855    46  8.4300000       8.31     11.47  8.4300000
## 856    46  8.4300000       8.31     11.47  8.4300000
## 857    46  8.4300000       8.31     11.47  8.4300000
## 858    46  8.4300000       8.31     11.47  8.4300000
## 859    47 53.8800000      53.50     56.66 53.8800000
## 860    47 53.8800000      53.50     56.66 53.8800000
## 861    47 53.8800000      53.50     56.66 53.8800000
## 862    47 53.8800000      53.50     56.66 53.8800000
## 863    47 53.8800000      53.50     56.66 53.8800000
## 864    47 53.8800000      53.50     56.66 53.8800000
## 865    47 53.8800000      53.50     56.66 53.8800000
## 866    47 53.8800000      53.50     56.66 53.8800000
## 867    47 53.8800000      53.50     56.66 53.8800000
## 868    47 53.8800000      53.50     56.66 53.8800000
## 869    47 53.8800000      53.50     56.66 53.8800000
## 870    47 53.8800000      53.50     56.66 53.8800000
## 871    47 53.8800000      53.50     56.66 53.8800000
## 872    48  6.0500000       7.55     10.90  6.0500000
## 873    48  6.0500000       7.55     10.90  6.0500000
## 874    48  6.0500000       7.55     10.90  6.0500000
## 875    48  6.0500000       7.55     10.90  6.0500000
## 876    48  6.0500000       7.55     10.90  6.0500000
## 877    48  6.0500000       7.55     10.90  6.0500000
## 878    48  6.0500000       7.55     10.90  6.0500000
## 879    48  6.0500000       7.55     10.90  6.0500000
## 880    48  6.0500000       7.55     10.90  6.0500000
## 881    48  6.0500000       7.55     10.90  6.0500000
## 882    48  6.0500000       7.55     10.90  6.0500000
## 883    48  6.0500000       7.55     10.90  6.0500000
## 884    48  6.0500000       7.55     10.90  6.0500000
## 885    49 22.5100000      23.51     26.70 22.5100000
## 886    49 22.5100000      23.51     26.70 22.5100000
## 887    49 22.5100000      23.51     26.70 22.5100000
## 888    49 22.5100000      23.51     26.70 22.5100000
## 889    49 22.5100000      23.51     26.70 22.5100000
## 890    49 22.5100000      23.51     26.70 22.5100000
## 891    49 22.5100000      23.51     26.70 22.5100000
## 892    49 22.5100000      23.51     26.70 22.5100000
## 893    49 22.5100000      23.51     26.70 22.5100000
## 894    49 22.5100000      23.51     26.70 22.5100000
## 895    49 22.5100000      23.51     26.70 22.5100000
## 896    49 22.5100000      23.51     26.70 22.5100000
## 897    49 22.5100000      23.51     26.70 22.5100000
## 898    50 50.2200000      48.77     46.03 50.2200000
## 899    50 50.2200000      48.77     46.03 50.2200000
## 900    50 50.2200000      48.77     46.03 50.2200000
## 901    50 50.2200000      48.77     46.03 50.2200000
## 902    50 50.2200000      48.77     46.03 50.2200000
## 903    50 50.2200000      48.77     46.03 50.2200000
## 904    50 50.2200000      48.77     46.03 50.2200000
## 905    50 50.2200000      48.77     46.03 50.2200000
## 906    50 50.2200000      48.77     46.03 50.2200000
## 907    50 50.2200000      48.77     46.03 50.2200000
## 908    50 50.2200000      48.77     46.03 50.2200000
## 909    50 50.2200000      48.77     46.03 50.2200000
## 910    50 50.2200000      48.77     46.03 50.2200000
## 911    51 37.8000000      37.99     40.33 37.8000000
## 912    51 37.8000000      37.99     40.33 37.8000000
## 913    51 37.8000000      37.99     40.33 37.8000000
## 914    51 37.8000000      37.99     40.33 37.8000000
## 915    51 37.8000000      37.99     40.33 37.8000000
## 916    51 37.8000000      37.99     40.33 37.8000000
## 917    51 37.8000000      37.99     40.33 37.8000000
## 918    51 37.8000000      37.99     40.33 37.8000000
## 919    51 37.8000000      37.99     40.33 37.8000000
## 920    51 37.8000000      37.99     40.33 37.8000000
## 921    51 37.8000000      37.99     40.33 37.8000000
## 922    51 37.8000000      37.99     40.33 37.8000000
## 923    51 37.8000000      37.99     40.33 37.8000000
## 924    52 66.7000000      68.05     69.75 66.7000000
## 925    52 66.7000000      68.05     69.75 66.7000000
## 926    52 66.7000000      68.05     69.75 66.7000000
## 927    52 66.7000000      68.05     69.75 66.7000000
## 928    52 66.7000000      68.05     69.75 66.7000000
## 929    52 66.7000000      68.05     69.75 66.7000000
## 930    52 66.7000000      68.05     69.75 66.7000000
## 931    52 66.7000000      68.05     69.75 66.7000000
## 932    52 66.7000000      68.05     69.75 66.7000000
## 933    52 66.7000000      68.05     69.75 66.7000000
## 934    52 66.7000000      68.05     69.75 66.7000000
## 935    52 66.7000000      68.05     69.75 66.7000000
## 936    52 66.7000000      68.05     69.75 66.7000000
## 937    53 37.0300000      38.65     36.56 37.0300000
## 938    53 37.0300000      38.65     36.56 37.0300000
## 939    53 37.0300000      38.65     36.56 37.0300000
## 940    53 37.0300000      38.65     36.56 37.0300000
## 941    53 37.0300000      38.65     36.56 37.0300000
## 942    53 37.0300000      38.65     36.56 37.0300000
## 943    53 37.0300000      38.65     36.56 37.0300000
## 944    53 37.0300000      38.65     36.56 37.0300000
## 945    53 37.0300000      38.65     36.56 37.0300000
## 946    53 37.0300000      38.65     36.56 37.0300000
## 947    53 37.0300000      38.65     36.56 37.0300000
## 948    53 37.0300000      38.65     36.56 37.0300000
## 949    53 37.0300000      38.65     36.56 37.0300000
## 950    54 15.4100000      15.03     17.58 15.4100000
## 951    54 15.4100000      15.03     17.58 15.4100000
## 952    54 15.4100000      15.03     17.58 15.4100000
## 953    54 15.4100000      15.03     17.58 15.4100000
## 954    54 15.4100000      15.03     17.58 15.4100000
## 955    54 15.4100000      15.03     17.58 15.4100000
## 956    54 15.4100000      15.03     17.58 15.4100000
## 957    54 15.4100000      15.03     17.58 15.4100000
## 958    54 15.4100000      15.03     17.58 15.4100000
## 959    54 15.4100000      15.03     17.58 15.4100000
## 960    54 15.4100000      15.03     17.58 15.4100000
## 961    54 15.4100000      15.03     17.58 15.4100000
## 962    54 15.4100000      15.03     17.58 15.4100000
## 963    55 35.3500000      34.52     35.15 35.3500000
## 964    55 35.3500000      34.52     35.15 35.3500000
## 965    55 35.3500000      34.52     35.15 35.3500000
## 966    55 35.3500000      34.52     35.15 35.3500000
## 967    55 35.3500000      34.52     35.15 35.3500000
## 968    55 35.3500000      34.52     35.15 35.3500000
## 969    55 35.3500000      34.52     35.15 35.3500000
## 970    55 35.3500000      34.52     35.15 35.3500000
## 971    55 35.3500000      34.52     35.15 35.3500000
## 972    55 35.3500000      34.52     35.15 35.3500000
## 973    55 35.3500000      34.52     35.15 35.3500000
## 974    55 35.3500000      34.52     35.15 35.3500000
## 975    55 35.3500000      34.52     35.15 35.3500000
## 976    56 29.0600000      28.91     30.18 29.0600000
## 977    56 29.0600000      28.91     30.18 29.0600000
## 978    56 29.0600000      28.91     30.18 29.0600000
## 979    56 29.0600000      28.91     30.18 29.0600000
## 980    56 29.0600000      28.91     30.18 29.0600000
## 981    56 29.0600000      28.91     30.18 29.0600000
## 982    56 29.0600000      28.91     30.18 29.0600000
## 983    56 29.0600000      28.91     30.18 29.0600000
## 984    56 29.0600000      28.91     30.18 29.0600000
## 985    56 29.0600000      28.91     30.18 29.0600000
## 986    56 29.0600000      28.91     30.18 29.0600000
## 987    56 29.0600000      28.91     30.18 29.0600000
## 988    56 29.0600000      28.91     30.18 29.0600000
## 989    57 48.4800000      48.05     50.68 48.4800000
## 990    57 48.4800000      48.05     50.68 48.4800000
## 991    57 48.4800000      48.05     50.68 48.4800000
## 992    57 48.4800000      48.05     50.68 48.4800000
## 993    57 48.4800000      48.05     50.68 48.4800000
## 994    57 48.4800000      48.05     50.68 48.4800000
## 995    57 48.4800000      48.05     50.68 48.4800000
## 996    57 48.4800000      48.05     50.68 48.4800000
## 997    57 48.4800000      48.05     50.68 48.4800000
## 998    57 48.4800000      48.05     50.68 48.4800000
## 999    57 48.4800000      48.05     50.68 48.4800000
## 1000   57 48.4800000      48.05     50.68 48.4800000
## 1001   57 48.4800000      48.05     50.68 48.4800000
## 1002   58 10.0200000       9.68     13.22 10.0200000
## 1003   58 10.0200000       9.68     13.22 10.0200000
## 1004   58 10.0200000       9.68     13.22 10.0200000
## 1005   58 10.0200000       9.68     13.22 10.0200000
## 1006   58 10.0200000       9.68     13.22 10.0200000
## 1007   58 10.0200000       9.68     13.22 10.0200000
## 1008   58 10.0200000       9.68     13.22 10.0200000
## 1009   58 10.0200000       9.68     13.22 10.0200000
## 1010   58 10.0200000       9.68     13.22 10.0200000
## 1011   58 10.0200000       9.68     13.22 10.0200000
## 1012   58 10.0200000       9.68     13.22 10.0200000
## 1013   58 10.0200000       9.68     13.22 10.0200000
## 1014   58 10.0200000       9.68     13.22 10.0200000
## 1015   59  1.1500000       1.44      1.00  1.1500000
## 1016   59  1.1500000       1.44      1.00  1.1500000
## 1017   59  1.1500000       1.44      1.00  1.1500000
## 1018   59  1.1500000       1.44      1.00  1.1500000
## 1019   59  1.1500000       1.44      1.00  1.1500000
## 1020   59  1.1500000       1.44      1.00  1.1500000
## 1021   59  1.1500000       1.44      1.00  1.1500000
## 1022   59  1.1500000       1.44      1.00  1.1500000
## 1023   59  1.1500000       1.44      1.00  1.1500000
## 1024   59  1.1500000       1.44      1.00  1.1500000
## 1025   59  1.1500000       1.44      1.00  1.1500000
## 1026   59  1.1500000       1.44      1.00  1.1500000
## 1027   59  1.1500000       1.44      1.00  1.1500000
## 1028    6 14.3000000      13.32     11.70 14.3000000
## 1029    6 14.3000000      13.32     11.70 14.3000000
## 1030    6 14.3000000      13.32     11.70 14.3000000
## 1031    6 14.3000000      13.32     11.70 14.3000000
## 1032    6 14.3000000      13.32     11.70 14.3000000
## 1033    6 14.3000000      13.32     11.70 14.3000000
## 1034    6 14.3000000      13.32     11.70 14.3000000
## 1035    6 14.3000000      13.32     11.70 14.3000000
## 1036    6 14.3000000      13.32     11.70 14.3000000
## 1037    6 14.3000000      13.32     11.70 14.3000000
## 1038    6 14.3000000      13.32     11.70 14.3000000
## 1039    6 14.3000000      13.32     11.70 14.3000000
## 1040    6 14.3000000      13.32     11.70 14.3000000
## 1041   60 32.4500000      33.21     32.29 32.4500000
## 1042   60 32.4500000      33.21     32.29 32.4500000
## 1043   60 32.4500000      33.21     32.29 32.4500000
## 1044   60 32.4500000      33.21     32.29 32.4500000
## 1045   60 32.4500000      33.21     32.29 32.4500000
## 1046   60 32.4500000      33.21     32.29 32.4500000
## 1047   60 32.4500000      33.21     32.29 32.4500000
## 1048   60 32.4500000      33.21     32.29 32.4500000
## 1049   60 32.4500000      33.21     32.29 32.4500000
## 1050   60 32.4500000      33.21     32.29 32.4500000
## 1051   60 32.4500000      33.21     32.29 32.4500000
## 1052   60 32.4500000      33.21     32.29 32.4500000
## 1053   60 32.4500000      33.21     32.29 32.4500000
## 1054   61 23.6400000      23.75     27.97 23.6400000
## 1055   61 23.6400000      23.75     27.97 23.6400000
## 1056   61 23.6400000      23.75     27.97 23.6400000
## 1057   61 23.6400000      23.75     27.97 23.6400000
## 1058   61 23.6400000      23.75     27.97 23.6400000
## 1059   61 23.6400000      23.75     27.97 23.6400000
## 1060   61 23.6400000      23.75     27.97 23.6400000
## 1061   61 23.6400000      23.75     27.97 23.6400000
## 1062   61 23.6400000      23.75     27.97 23.6400000
## 1063   61 23.6400000      23.75     27.97 23.6400000
## 1064   61 23.6400000      23.75     27.97 23.6400000
## 1065   61 23.6400000      23.75     27.97 23.6400000
## 1066   61 23.6400000      23.75     27.97 23.6400000
## 1067   62 13.1000000      13.91     13.28 13.1000000
## 1068   62 13.1000000      13.91     13.28 13.1000000
## 1069   62 13.1000000      13.91     13.28 13.1000000
## 1070   62 13.1000000      13.91     13.28 13.1000000
## 1071   62 13.1000000      13.91     13.28 13.1000000
## 1072   62 13.1000000      13.91     13.28 13.1000000
## 1073   62 13.1000000      13.91     13.28 13.1000000
## 1074   62 13.1000000      13.91     13.28 13.1000000
## 1075   62 13.1000000      13.91     13.28 13.1000000
## 1076   62 13.1000000      13.91     13.28 13.1000000
## 1077   62 13.1000000      13.91     13.28 13.1000000
## 1078   62 13.1000000      13.91     13.28 13.1000000
## 1079   62 13.1000000      13.91     13.28 13.1000000
## 1080   63 49.8000000      49.86     48.71 49.8000000
## 1081   63 49.8000000      49.86     48.71 49.8000000
## 1082   63 49.8000000      49.86     48.71 49.8000000
## 1083   63 49.8000000      49.86     48.71 49.8000000
## 1084   63 49.8000000      49.86     48.71 49.8000000
## 1085   63 49.8000000      49.86     48.71 49.8000000
## 1086   63 49.8000000      49.86     48.71 49.8000000
## 1087   63 49.8000000      49.86     48.71 49.8000000
## 1088   63 49.8000000      49.86     48.71 49.8000000
## 1089   63 49.8000000      49.86     48.71 49.8000000
## 1090   63 49.8000000      49.86     48.71 49.8000000
## 1091   63 49.8000000      49.86     48.71 49.8000000
## 1092   63 49.8000000      49.86     48.71 49.8000000
## 1093   64 11.6500000      12.31     10.33 11.6500000
## 1094   64 11.6500000      12.31     10.33 11.6500000
## 1095   64 11.6500000      12.31     10.33 11.6500000
## 1096   64 11.6500000      12.31     10.33 11.6500000
## 1097   64 11.6500000      12.31     10.33 11.6500000
## 1098   64 11.6500000      12.31     10.33 11.6500000
## 1099   64 11.6500000      12.31     10.33 11.6500000
## 1100   64 11.6500000      12.31     10.33 11.6500000
## 1101   64 11.6500000      12.31     10.33 11.6500000
## 1102   64 11.6500000      12.31     10.33 11.6500000
## 1103   64 11.6500000      12.31     10.33 11.6500000
## 1104   64 11.6500000      12.31     10.33 11.6500000
## 1105   64 11.6500000      12.31     10.33 11.6500000
## 1106   65 18.3600000      18.62     16.06 18.3600000
## 1107   65 18.3600000      18.62     16.06 18.3600000
## 1108   65 18.3600000      18.62     16.06 18.3600000
## 1109   65 18.3600000      18.62     16.06 18.3600000
## 1110   65 18.3600000      18.62     16.06 18.3600000
## 1111   65 18.3600000      18.62     16.06 18.3600000
## 1112   65 18.3600000      18.62     16.06 18.3600000
## 1113   65 18.3600000      18.62     16.06 18.3600000
## 1114   65 18.3600000      18.62     16.06 18.3600000
## 1115   65 18.3600000      18.62     16.06 18.3600000
## 1116   65 18.3600000      18.62     16.06 18.3600000
## 1117   65 18.3600000      18.62     16.06 18.3600000
## 1118   65 18.3600000      18.62     16.06 18.3600000
## 1119   68  2.6400000       2.55      3.38  2.6400000
## 1120   68  2.6400000       2.55      3.38  2.6400000
## 1121   68  2.6400000       2.55      3.38  2.6400000
## 1122   68  2.6400000       2.55      3.38  2.6400000
## 1123   68  2.6400000       2.55      3.38  2.6400000
## 1124   68  2.6400000       2.55      3.38  2.6400000
## 1125   68  2.6400000       2.55      3.38  2.6400000
## 1126   68  2.6400000       2.55      3.38  2.6400000
## 1127   68  2.6400000       2.55      3.38  2.6400000
## 1128   68  2.6400000       2.55      3.38  2.6400000
## 1129   68  2.6400000       2.55      3.38  2.6400000
## 1130   68  2.6400000       2.55      3.38  2.6400000
## 1131   68  2.6400000       2.55      3.38  2.6400000
## 1132    7  3.7800000       3.30      3.11  3.7800000
## 1133    7  3.7800000       3.30      3.11  3.7800000
## 1134    7  3.7800000       3.30      3.11  3.7800000
## 1135    7  3.7800000       3.30      3.11  3.7800000
## 1136    7  3.7800000       3.30      3.11  3.7800000
## 1137    7  3.7800000       3.30      3.11  3.7800000
## 1138    7  3.7800000       3.30      3.11  3.7800000
## 1139    7  3.7800000       3.30      3.11  3.7800000
## 1140    7  3.7800000       3.30      3.11  3.7800000
## 1141    7  3.7800000       3.30      3.11  3.7800000
## 1142    7  3.7800000       3.30      3.11  3.7800000
## 1143    7  3.7800000       3.30      3.11  3.7800000
## 1144    7  3.7800000       3.30      3.11  3.7800000
## 1145   70 11.7900000      12.52     13.70 11.7900000
## 1146   70 11.7900000      12.52     13.70 11.7900000
## 1147   70 11.7900000      12.52     13.70 11.7900000
## 1148   70 11.7900000      12.52     13.70 11.7900000
## 1149   70 11.7900000      12.52     13.70 11.7900000
## 1150   70 11.7900000      12.52     13.70 11.7900000
## 1151   70 11.7900000      12.52     13.70 11.7900000
## 1152   70 11.7900000      12.52     13.70 11.7900000
## 1153   70 11.7900000      12.52     13.70 11.7900000
## 1154   70 11.7900000      12.52     13.70 11.7900000
## 1155   70 11.7900000      12.52     13.70 11.7900000
## 1156   70 11.7900000      12.52     13.70 11.7900000
## 1157   70 11.7900000      12.52     13.70 11.7900000
## 1158   72 37.8300000      38.33     36.45 37.8300000
## 1159   72 37.8300000      38.33     36.45 37.8300000
## 1160   72 37.8300000      38.33     36.45 37.8300000
## 1161   72 37.8300000      38.33     36.45 37.8300000
## 1162   72 37.8300000      38.33     36.45 37.8300000
## 1163   72 37.8300000      38.33     36.45 37.8300000
## 1164   72 37.8300000      38.33     36.45 37.8300000
## 1165   72 37.8300000      38.33     36.45 37.8300000
## 1166   72 37.8300000      38.33     36.45 37.8300000
## 1167   72 37.8300000      38.33     36.45 37.8300000
## 1168   72 37.8300000      38.33     36.45 37.8300000
## 1169   72 37.8300000      38.33     36.45 37.8300000
## 1170   72 37.8300000      38.33     36.45 37.8300000
## 1171   73 38.4500000      39.29     35.31 38.4500000
## 1172   73 38.4500000      39.29     35.31 38.4500000
## 1173   73 38.4500000      39.29     35.31 38.4500000
## 1174   73 38.4500000      39.29     35.31 38.4500000
## 1175   73 38.4500000      39.29     35.31 38.4500000
## 1176   73 38.4500000      39.29     35.31 38.4500000
## 1177   73 38.4500000      39.29     35.31 38.4500000
## 1178   73 38.4500000      39.29     35.31 38.4500000
## 1179   73 38.4500000      39.29     35.31 38.4500000
## 1180   73 38.4500000      39.29     35.31 38.4500000
## 1181   73 38.4500000      39.29     35.31 38.4500000
## 1182   73 38.4500000      39.29     35.31 38.4500000
## 1183   73 38.4500000      39.29     35.31 38.4500000
## 1184   74  1.2600000       1.37      1.76  1.2600000
## 1185   74  1.2600000       1.37      1.76  1.2600000
## 1186   74  1.2600000       1.37      1.76  1.2600000
## 1187   74  1.2600000       1.37      1.76  1.2600000
## 1188   74  1.2600000       1.37      1.76  1.2600000
## 1189   74  1.2600000       1.37      1.76  1.2600000
## 1190   74  1.2600000       1.37      1.76  1.2600000
## 1191   74  1.2600000       1.37      1.76  1.2600000
## 1192   74  1.2600000       1.37      1.76  1.2600000
## 1193   74  1.2600000       1.37      1.76  1.2600000
## 1194   74  1.2600000       1.37      1.76  1.2600000
## 1195   74  1.2600000       1.37      1.76  1.2600000
## 1196   74  1.2600000       1.37      1.76  1.2600000
## 1197   75 71.5100000      72.21     68.56 71.5100000
## 1198   75 71.5100000      72.21     68.56 71.5100000
## 1199   75 71.5100000      72.21     68.56 71.5100000
## 1200   75 71.5100000      72.21     68.56 71.5100000
## 1201   75 71.5100000      72.21     68.56 71.5100000
## 1202   75 71.5100000      72.21     68.56 71.5100000
## 1203   75 71.5100000      72.21     68.56 71.5100000
## 1204   75 71.5100000      72.21     68.56 71.5100000
## 1205   75 71.5100000      72.21     68.56 71.5100000
## 1206   75 71.5100000      72.21     68.56 71.5100000
## 1207   75 71.5100000      72.21     68.56 71.5100000
## 1208   75 71.5100000      72.21     68.56 71.5100000
## 1209   75 71.5100000      72.21     68.56 71.5100000
## 1210   76 10.1100000      11.60      8.80 10.1100000
## 1211   76 10.1100000      11.60      8.80 10.1100000
## 1212   76 10.1100000      11.60      8.80 10.1100000
## 1213   76 10.1100000      11.60      8.80 10.1100000
## 1214   76 10.1100000      11.60      8.80 10.1100000
## 1215   76 10.1100000      11.60      8.80 10.1100000
## 1216   76 10.1100000      11.60      8.80 10.1100000
## 1217   76 10.1100000      11.60      8.80 10.1100000
## 1218   76 10.1100000      11.60      8.80 10.1100000
## 1219   76 10.1100000      11.60      8.80 10.1100000
## 1220   76 10.1100000      11.60      8.80 10.1100000
## 1221   76 10.1100000      11.60      8.80 10.1100000
## 1222   76 10.1100000      11.60      8.80 10.1100000
## 1223   77 29.0800000      29.99     35.11 29.0800000
## 1224   77 29.0800000      29.99     35.11 29.0800000
## 1225   77 29.0800000      29.99     35.11 29.0800000
## 1226   77 29.0800000      29.99     35.11 29.0800000
## 1227   77 29.0800000      29.99     35.11 29.0800000
## 1228   77 29.0800000      29.99     35.11 29.0800000
## 1229   77 29.0800000      29.99     35.11 29.0800000
## 1230   77 29.0800000      29.99     35.11 29.0800000
## 1231   77 29.0800000      29.99     35.11 29.0800000
## 1232   77 29.0800000      29.99     35.11 29.0800000
## 1233   77 29.0800000      29.99     35.11 29.0800000
## 1234   77 29.0800000      29.99     35.11 29.0800000
## 1235   77 29.0800000      29.99     35.11 29.0800000
## 1236   79 39.5800000      38.84     38.38 39.5800000
## 1237   79 39.5800000      38.84     38.38 39.5800000
## 1238   79 39.5800000      38.84     38.38 39.5800000
## 1239   79 39.5800000      38.84     38.38 39.5800000
## 1240   79 39.5800000      38.84     38.38 39.5800000
## 1241   79 39.5800000      38.84     38.38 39.5800000
## 1242   79 39.5800000      38.84     38.38 39.5800000
## 1243   79 39.5800000      38.84     38.38 39.5800000
## 1244   79 39.5800000      38.84     38.38 39.5800000
## 1245   79 39.5800000      38.84     38.38 39.5800000
## 1246   79 39.5800000      38.84     38.38 39.5800000
## 1247   79 39.5800000      38.84     38.38 39.5800000
## 1248   79 39.5800000      38.84     38.38 39.5800000
## 1249    8 17.5300000      17.04     17.35 17.5300000
## 1250    8 17.5300000      17.04     17.35 17.5300000
## 1251    8 17.5300000      17.04     17.35 17.5300000
## 1252    8 17.5300000      17.04     17.35 17.5300000
## 1253    8 17.5300000      17.04     17.35 17.5300000
## 1254    8 17.5300000      17.04     17.35 17.5300000
## 1255    8 17.5300000      17.04     17.35 17.5300000
## 1256    8 17.5300000      17.04     17.35 17.5300000
## 1257    8 17.5300000      17.04     17.35 17.5300000
## 1258    8 17.5300000      17.04     17.35 17.5300000
## 1259    8 17.5300000      17.04     17.35 17.5300000
## 1260    8 17.5300000      17.04     17.35 17.5300000
## 1261    8 17.5300000      17.04     17.35 17.5300000
## 1262   80 60.8500000      60.29     62.05 60.8500000
## 1263   80 60.8500000      60.29     62.05 60.8500000
## 1264   80 60.8500000      60.29     62.05 60.8500000
## 1265   80 60.8500000      60.29     62.05 60.8500000
## 1266   80 60.8500000      60.29     62.05 60.8500000
## 1267   80 60.8500000      60.29     62.05 60.8500000
## 1268   80 60.8500000      60.29     62.05 60.8500000
## 1269   80 60.8500000      60.29     62.05 60.8500000
## 1270   80 60.8500000      60.29     62.05 60.8500000
## 1271   80 60.8500000      60.29     62.05 60.8500000
## 1272   80 60.8500000      60.29     62.05 60.8500000
## 1273   80 60.8500000      60.29     62.05 60.8500000
## 1274   80 60.8500000      60.29     62.05 60.8500000
## 1275   81 63.9100000      64.62     67.52 63.9100000
## 1276   81 63.9100000      64.62     67.52 63.9100000
## 1277   81 63.9100000      64.62     67.52 63.9100000
## 1278   81 63.9100000      64.62     67.52 63.9100000
## 1279   81 63.9100000      64.62     67.52 63.9100000
## 1280   81 63.9100000      64.62     67.52 63.9100000
## 1281   81 63.9100000      64.62     67.52 63.9100000
## 1282   81 63.9100000      64.62     67.52 63.9100000
## 1283   81 63.9100000      64.62     67.52 63.9100000
## 1284   81 63.9100000      64.62     67.52 63.9100000
## 1285   81 63.9100000      64.62     67.52 63.9100000
## 1286   81 63.9100000      64.62     67.52 63.9100000
## 1287   81 63.9100000      64.62     67.52 63.9100000
## 1288   82 75.8200000      74.19     76.76 75.8200000
## 1289   82 75.8200000      74.19     76.76 75.8200000
## 1290   82 75.8200000      74.19     76.76 75.8200000
## 1291   82 75.8200000      74.19     76.76 75.8200000
## 1292   82 75.8200000      74.19     76.76 75.8200000
## 1293   82 75.8200000      74.19     76.76 75.8200000
## 1294   82 75.8200000      74.19     76.76 75.8200000
## 1295   82 75.8200000      74.19     76.76 75.8200000
## 1296   82 75.8200000      74.19     76.76 75.8200000
## 1297   82 75.8200000      74.19     76.76 75.8200000
## 1298   82 75.8200000      74.19     76.76 75.8200000
## 1299   82 75.8200000      74.19     76.76 75.8200000
## 1300   82 75.8200000      74.19     76.76 75.8200000
## 1301   83  3.8000000       3.97      1.00  3.8000000
## 1302   83  3.8000000       3.97      1.00  3.8000000
## 1303   83  3.8000000       3.97      1.00  3.8000000
## 1304   83  3.8000000       3.97      1.00  3.8000000
## 1305   83  3.8000000       3.97      1.00  3.8000000
## 1306   83  3.8000000       3.97      1.00  3.8000000
## 1307   83  3.8000000       3.97      1.00  3.8000000
## 1308   83  3.8000000       3.97      1.00  3.8000000
## 1309   83  3.8000000       3.97      1.00  3.8000000
## 1310   83  3.8000000       3.97      1.00  3.8000000
## 1311   83  3.8000000       3.97      1.00  3.8000000
## 1312   83  3.8000000       3.97      1.00  3.8000000
## 1313   83  3.8000000       3.97      1.00  3.8000000
## 1314   84 83.9900000      83.54     84.10 83.9900000
## 1315   84 83.9900000      83.54     84.10 83.9900000
## 1316   84 83.9900000      83.54     84.10 83.9900000
## 1317   84 83.9900000      83.54     84.10 83.9900000
## 1318   84 83.9900000      83.54     84.10 83.9900000
## 1319   84 83.9900000      83.54     84.10 83.9900000
## 1320   84 83.9900000      83.54     84.10 83.9900000
## 1321   84 83.9900000      83.54     84.10 83.9900000
## 1322   84 83.9900000      83.54     84.10 83.9900000
## 1323   84 83.9900000      83.54     84.10 83.9900000
## 1324   84 83.9900000      83.54     84.10 83.9900000
## 1325   84 83.9900000      83.54     84.10 83.9900000
## 1326   84 83.9900000      83.54     84.10 83.9900000
## 1327   86 66.3500000      66.98     68.92 66.3500000
## 1328   86 66.3500000      66.98     68.92 66.3500000
## 1329   86 66.3500000      66.98     68.92 66.3500000
## 1330   86 66.3500000      66.98     68.92 66.3500000
## 1331   86 66.3500000      66.98     68.92 66.3500000
## 1332   86 66.3500000      66.98     68.92 66.3500000
## 1333   86 66.3500000      66.98     68.92 66.3500000
## 1334   86 66.3500000      66.98     68.92 66.3500000
## 1335   86 66.3500000      66.98     68.92 66.3500000
## 1336   86 66.3500000      66.98     68.92 66.3500000
## 1337   86 66.3500000      66.98     68.92 66.3500000
## 1338   86 66.3500000      66.98     68.92 66.3500000
## 1339   86 66.3500000      66.98     68.92 66.3500000
## 1340   87 42.8400000      41.87     44.72 42.8400000
## 1341   87 42.8400000      41.87     44.72 42.8400000
## 1342   87 42.8400000      41.87     44.72 42.8400000
## 1343   87 42.8400000      41.87     44.72 42.8400000
## 1344   87 42.8400000      41.87     44.72 42.8400000
## 1345   87 42.8400000      41.87     44.72 42.8400000
## 1346   87 42.8400000      41.87     44.72 42.8400000
## 1347   87 42.8400000      41.87     44.72 42.8400000
## 1348   87 42.8400000      41.87     44.72 42.8400000
## 1349   87 42.8400000      41.87     44.72 42.8400000
## 1350   87 42.8400000      41.87     44.72 42.8400000
## 1351   87 42.8400000      41.87     44.72 42.8400000
## 1352   87 42.8400000      41.87     44.72 42.8400000
## 1353   88 59.0100000      58.44     57.79 59.0100000
## 1354   88 59.0100000      58.44     57.79 59.0100000
## 1355   88 59.0100000      58.44     57.79 59.0100000
## 1356   88 59.0100000      58.44     57.79 59.0100000
## 1357   88 59.0100000      58.44     57.79 59.0100000
## 1358   88 59.0100000      58.44     57.79 59.0100000
## 1359   88 59.0100000      58.44     57.79 59.0100000
## 1360   88 59.0100000      58.44     57.79 59.0100000
## 1361   88 59.0100000      58.44     57.79 59.0100000
## 1362   88 59.0100000      58.44     57.79 59.0100000
## 1363   88 59.0100000      58.44     57.79 59.0100000
## 1364   88 59.0100000      58.44     57.79 59.0100000
## 1365   88 59.0100000      58.44     57.79 59.0100000
# length(unique(data_xy$sev))
summary(data_xy$sev)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.42    8.50   19.07   25.20   37.83   83.99

Images

hist_sev_xy =  data_xy %>% 
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean) %>%
  ggplot(aes(sev))+
  geom_histogram(color = "white", fill = "black", bins = 20)+
  theme_minimal_hgrid(font_size = 10)+
  labs(x = "Severity (%)",
       y = "Frequency")+
  scale_x_continuous(limits = c(-5,105), breaks = seq(0,100,25))+
  # theme_void()+
  # coord_fixed()+
  theme(panel.background = element_rect(color = "black"))
EX.L1<-stack(paste("./pics/01-Xylella-tobacco-bg-white/","75.jpg",sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)
## [1] "3 layers available"
EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)
## [1] "3 layers available"
EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=200, cropAbove=T, plot = F)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)
## [1] "3 layers available"
# plot(EX.L4$HUE)
rgb_fig_xy = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"))
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
gli_fig_xy = as.data.frame(EX.L4$HUE, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = HUE))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"),
        legend.title = element_text(size = 8),
        legend.text = element_text(size = 8))

# rgb_fig_xy+ gli_fig_xy
# rgb_fig_sbr + gli_fig_sbr + hist_sev_sbr #+
#   rgb_fig_wlb + gli_fig_wlb + hist_sev_WLB+
  rgb_fig_xy + gli_fig_xy +hist_sev_xy
## Warning: Removed 2 rows containing missing values (geom_bar).

#    plot_layout(widths = c(1, 1, 1),
#                heights = c(1,1,1))
# 
# ggsave("figs/leaf_gli.png",dpi = 600, height = 7, width =8)

Relationship sev indices

rgb_gg_xy = data_xy %>% 
  filter(index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev, color = index)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =1)+
  scale_color_manual(values = c("steelblue","darkgreen", "darkred"))+
  theme_minimal_hgrid()+
  labs(x = "Mean value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))+
  theme(legend.position = "none")
rgb_gg_xy
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

index_gg_xy = data_xy %>% 
  filter(!index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(color = "black", se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =2)+
  theme_minimal_hgrid()+
  labs(x = "Mean index value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))
index_gg_xy
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plot_grid(
  plot_grid(NULL,rgb_gg_xy,NULL, rel_widths =c(0.18,1,0.2), nrow = 1),
          index_gg_xy,
          nrow = 2,
          rel_heights = c(0.5,1))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggsave("figs/index_sev_XY.png", dpi = 500, height = 8, width = 10)
cor_xy = data_xy %>% 
  group_by(index) %>% 
  dplyr::summarise(cor = round(  cor.test(mean,sev, method = "spearman")$estimate,3),
                   P_value = round(cor.test(mean,sev, method = "spearman")$p.value,4)) %>% 
  arrange(-cor)
## `summarise()` ungrouping output (override with `.groups` argument)
cor_xy
## # A tibble: 13 x 3
##    index    cor P_value
##    <chr>  <dbl>   <dbl>
##  1 HUE    0.694  0     
##  2 HI     0.627  0     
##  3 SCI    0.623  0     
##  4 SI     0.356  0.0002
##  5 Red    0.286  0.0032
##  6 BI     0.219  0.0252
##  7 BGI    0.214  0.0288
##  8 Blue   0.195  0.0463
##  9 gray   0.194  0.0477
## 10 Green  0.121  0.217 
## 11 GLI   -0.49   0     
## 12 NGRDI -0.623  0     
## 13 VARI  -0.624  0

Spread df

all_data_spread = data_xy %>% 
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean)   

all_data_spread
## # A tibble: 105 x 15
##    file    sev   BGI    BI  Blue   GLI  gray Green    HI    HUE    NGRDI   Red
##    <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>    <dbl> <dbl>
##  1 1     26.8  0.544  167. 106.  0.139  182.  193. 0.868 -1.23   0.0151   187.
##  2 10    24.3  0.523  162.  99.4 0.149  176.  189. 0.829 -1.31   0.0208   181.
##  3 11    16.3  0.477  135.  78.5 0.184  148.  163. 0.632 -1.57   0.0508   147.
##  4 12    14.8  0.547  163. 103.  0.138  177.  188. 0.863 -1.18   0.0158   182.
##  5 126    7.92 0.640  188. 135.  0.100  201.  210. 0.995 -0.634  0.00123  210.
##  6 127    9.48 0.582  177. 118.  0.125  191.  202. 0.900 -1.12   0.0124   198.
##  7 128    9.39 0.509  145.  87.0 0.157  158.  170. 0.794 -1.47   0.0260   161.
##  8 129    0.49 0.514  121.  76.6 0.192  133.  148. 0.360 -1.57   0.0845   125.
##  9 13    13.6  0.488  129.  77.1 0.183  143.  156. 0.599 -1.56   0.0546   140.
## 10 130   47.8  0.603  176. 118.  0.102  189.  196. 1.15   0.122 -0.0137   201.
## # ... with 95 more rows, and 3 more variables: SCI <dbl>, SI <dbl>, VARI <dbl>

GBM

train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.75*length(all_data_spread$sev),1))
# length(train)
gbm.fit = gbm(sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI,
             data = all_data_spread[train,],
             distribution = "gaussian",
              n.trees = 1000,
             interaction.depth = 3,
             shrinkage = 0.1,
             cv.folds = 5,
             n.cores = NULL, # will use all cores by default
             verbose = FALSE)
print(gbm.fit)
## gbm(formula = sev ~ BGI + BI + GLI + HI + HUE + NGRDI + VARI + 
##     gray + Red + Green + Blue + SI + SCI, distribution = "gaussian", 
##     data = all_data_spread[train, ], n.trees = 1000, interaction.depth = 3, 
##     shrinkage = 0.1, cv.folds = 5, verbose = FALSE, n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 1000 iterations were performed.
## The best cross-validation iteration was 231.
## There were 13 predictors of which 13 had non-zero influence.
sqrt(min(gbm.fit$cv.error))
## [1] 12.43899
gbm.perf(gbm.fit, method = "cv")

## [1] 231
# find index for n trees with minimum CV error
min_MSE <- which.min(gbm.fit$cv.error)
sqrt(gbm.fit$cv.error[min_MSE])
## [1] 12.43899
# best.iter <- gbm.perf(model1, method = "test")
# print(best.iter)

pred = predict(gbm.fit, newdata = all_data_spread[-train,-1], ntrees = 5000 )
## Using 231 trees...
sqrt(mean(((pred)-all_data_spread$sev[-train])^2))
## [1] 11.5175
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.6909319
plot((pred), (pred)-all_data_spread$sev[-train])
abline(a=0,b=0)

Testing various hyperparameters

Create hyperparameter grid

hyper_grid <- expand.grid(
  shrinkage = c(.001, .01, .1, .3),
  interaction.depth = c(1, 3, 5, 6),
  n.minobsinnode = c(5, 10, 15),
  bag.fraction = c(.5,.65, .8, 1), 
  optimal_trees = 0,               # a place to dump results
  min_RMSE = 0,
  CCC =0 # a place to dump results
)
# total number of combinations
nrow(hyper_grid)
## [1] 192
# randomize data
set.seed(123)
train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.80*length(all_data_spread$sev),1))

# grid search 
for(i in 1:nrow(hyper_grid)) {

# reproducibility
set.seed(123)


 # train model
gbm.tune <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray +Red+Green+Blue + SI + SCI, #<<<<<
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = hyper_grid$interaction.depth[i],
  shrinkage = hyper_grid$shrinkage[i],
  n.minobsinnode = hyper_grid$n.minobsinnode[i],
  bag.fraction = hyper_grid$bag.fraction[i],
  train.fraction = .75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE)

pred = predict(gbm.tune, newdata = all_data_spread[-train,-1], ntrees = 5000 )
 # add min training error and trees to grid
  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$valid.error))
  hyper_grid$CCC[i] = CCC(pred, all_data_spread$sev[-train])$rho.c$est#<<<<<
  
}
## Using 4918 trees...
## Using 506 trees...
## Using 53 trees...
## Using 14 trees...
## Using 2081 trees...
## Using 191 trees...
## Using 18 trees...
## Using 13 trees...
## Using 2081 trees...
## Using 191 trees...
## Using 19 trees...
## Using 9 trees...
## Using 2081 trees...
## Using 191 trees...
## Using 19 trees...
## Using 9 trees...
## Using 4991 trees...
## Using 680 trees...
## Using 53 trees...
## Using 58 trees...
## Using 4974 trees...
## Using 530 trees...
## Using 53 trees...
## Using 60 trees...
## Using 4974 trees...
## Using 530 trees...
## Using 53 trees...
## Using 60 trees...
## Using 4974 trees...
## Using 530 trees...
## Using 53 trees...
## Using 60 trees...
## Using 4986 trees...
## Using 658 trees...
## Using 89 trees...
## Using 135 trees...
## Using 4986 trees...
## Using 658 trees...
## Using 89 trees...
## Using 135 trees...
## Using 4986 trees...
## Using 658 trees...
## Using 89 trees...
## Using 135 trees...
## Using 4986 trees...
## Using 658 trees...
## Using 89 trees...
## Using 135 trees...
## Using 4990 trees...
## Using 966 trees...
## Using 64 trees...
## Using 10 trees...
## Using 1956 trees...
## Using 170 trees...
## Using 19 trees...
## 
## Using 19 trees...
## Using 1646 trees...
## Using 166 trees...
## Using 16 trees...
## Using 4662 trees...
## Using 1585 trees...
## Using 166 trees...
## Using 16 trees...
## Using 25 trees...
## Using 4748 trees...
## Using 498 trees...
## Using 54 trees...
## Using 16 trees...
## Using 2691 trees...
## Using 279 trees...
## Using 35 trees...
## Using 9 trees...
## Using 2691 trees...
## Using 279 trees...
## Using 35 trees...
## Using 9 trees...
## Using 2691 trees...
## Using 279 trees...
## Using 35 trees...
## Using 9 trees...
## Using 4987 trees...
## Using 927 trees...
## Using 96 trees...
## Using 26 trees...
## Using 4987 trees...
## Using 927 trees...
## Using 96 trees...
## Using 26 trees...
## Using 4987 trees...
## Using 927 trees...
## Using 96 trees...
## Using 26 trees...
## Using 4987 trees...
## Using 927 trees...
## Using 96 trees...
## Using 26 trees...
## Using 4969 trees...
## Using 928 trees...
## Using 52 trees...
## Using 23 trees...
## Using 1581 trees...
## Using 152 trees...
## Using 4993 trees...
## Using 5 trees...
## Using 1333 trees...
## Using 96 trees...
## Using 11 trees...
## Using 4 trees...
## Using 1312 trees...
## Using 94 trees...
## Using 11 trees...
## Using 4 trees...
## Using 4404 trees...
## Using 380 trees...
## Using 35 trees...
## Using 13 trees...
## Using 2265 trees...
## Using 207 trees...
## Using 25 trees...
## Using 4 trees...
## Using 2265 trees...
## Using 207 trees...
## Using 28 trees...
## Using 4 trees...
## Using 2265 trees...
## Using 207 trees...
## Using 28 trees...
## Using 4 trees...
## Using 4998 trees...
## Using 863 trees...
## Using 55 trees...
## Using 30 trees...
## Using 4608 trees...
## Using 429 trees...
## Using 56 trees...
## Using 18 trees...
## Using 4608 trees...
## Using 429 trees...
## Using 56 trees...
## Using 18 trees...
## Using 4608 trees...
## Using 429 trees...
## Using 56 trees...
## Using 18 trees...
## Using 5000 trees...
## Using 2091 trees...
## Using 218 trees...
## Using 59 trees...
## Using 2167 trees...
## Using 203 trees...
## Using 18 trees...
## Using 3 trees...
## Using 894 trees...
## Using 88 trees...
## Using 8 trees...
## Using 2 trees...
## Using 772 trees...
## Using 74 trees...
## Using 9 trees...
## Using 2 trees...
## Using 5000 trees...
## Using 630 trees...
## Using 63 trees...
## Using 13 trees...
## Using 2458 trees...
## Using 250 trees...
## Using 23 trees...
## Using 6 trees...
## Using 2392 trees...
## Using 235 trees...
## Using 21 trees...
## Using 7 trees...
## Using 2392 trees...
## Using 235 trees...
## Using 21 trees...
## Using 7 trees...
## Using 5000 trees...
## Using 719 trees...
## Using 76 trees...
## Using 29 trees...
## Using 3351 trees...
## Using 331 trees...
## Using 27 trees...
## Using 6 trees...
## Using 3351 trees...
## Using 331 trees...
## Using 27 trees...
## Using 6 trees...
## Using 3351 trees...
## Using 331 trees...
## Using 27 trees...
## Using 6 trees...
best_par = hyper_grid %>% 
  dplyr::arrange(-CCC) %>%
  head(10)
best_par
##    shrinkage interaction.depth n.minobsinnode bag.fraction optimal_trees
## 1       0.30                 3              5         0.65            19
## 2       0.30                 5              5         0.65          4662
## 3       0.01                 1              5         0.65           966
## 4       0.30                 6              5         0.65            25
## 5       0.01                 1              5         1.00          2091
## 6       0.01                 1              5         0.80           928
## 7       0.30                 1              5         0.80            23
## 8       0.30                 1              5         1.00            59
## 9       0.10                 1              5         1.00           218
## 10      0.10                 1              5         0.65            64
##    min_RMSE       CCC
## 1  11.37018 0.8649715
## 2  12.21829 0.8407627
## 3  12.00979 0.8362572
## 4  12.57791 0.8356177
## 5  12.73349 0.8252694
## 6  12.61867 0.8244094
## 7  12.65166 0.8236509
## 8  12.65081 0.8226995
## 9  12.83123 0.8215836
## 10 12.07186 0.8157707
# gbm.tune$fit

Best model

# for reproducibility
set.seed(123)

# train GBM model
gbm.fit.final <- gbm(
  formula = (sev) ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+Red+Green+Blue+gray+SI+SCI,
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = best_par$optimal_trees[1],
  interaction.depth = best_par$interaction.depth[1],
  shrinkage = best_par$shrinkage[1],
  n.minobsinnode = best_par$n.minobsinnode[1],
  bag.fraction = best_par$bag.fraction[1], 
  train.fraction =0.75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE
  )

Relative influence

par(mar = c(5, 8, 1, 1))
summary_gbm_xy = summary(
  gbm.fit.final, 
  cBars = 15,
  method = relative.influence, # also can use permutation.test.gbm
  las = 2
  )

rel_xy = summary_gbm_xy %>% 
  rownames_to_column("index") %>% 
  ggplot(aes(rel.inf, reorder(var, rel.inf)))+
  geom_col(aes(fill =rel.inf>1, color =rel.inf>1 ), width = 0.85)+
  theme_minimal_vgrid()+
  labs(x = "Relative influence (%)",
       y = "Model predictors",
       fill = "RI > 1%",
       color = "RI > 1%")
rel_xy

# ggsave("figs/var_influence.png",dpi = 600, height = 4, width = 6)

Partial dependence plots

gbm.fit.final %>%
  pdp::partial(pred.var = "HUE", n.trees = gbm.fit.final$n.trees, grid.resolution = 100) %>%
  ggplot(aes( HUE,(yhat)))+
  geom_line()

LIME

library(lime)
model_type.gbm <- function(x, ...) {
  return("regression")
}

predict_model.gbm <- function(x, newdata, ...) {
  pred <- predict(x, newdata, n.trees = x$n.trees)
  return(as.data.frame(pred))
}
# get a few observations to perform local interpretation on
local_obs <- (all_data_spread[-train,])[1:4, ]

# apply LIME
explainer <- lime(all_data_spread[train,], gbm.fit.final)
explanation <- lime::explain(local_obs, explainer, n_features = 7, n.trees =1)
plot_features(explanation)

Prediction

# predict values for test data
pred <- predict(gbm.fit.final,
                n.trees = gbm.fit.final$n.trees,
                all_data_spread[-train,])

# results
caret::RMSE((pred), all_data_spread[-train,]$sev)
## [1] 10.55157
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.8649715
cor((pred), all_data_spread$sev[-train])^2
## [1] 0.757813
accuracy_xy =data.frame(predi=pred, actual = all_data_spread$sev[-train]) %>% 
  summarise(RMSE = caret::RMSE(pred, actual),
            r = cor(pred, actual),
            s.shift = CCC(pred, actual)$s.shift,
            l.shift = CCC(pred, actual)$l.shift,
            C.b = CCC(pred, actual)$C.b,
            CCC = CCC(pred, actual)$rho.c$est,
            CIS = paste(
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[2],2),","," ",
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[3],2),sep = ""
  ))
accuracy_xy
##       RMSE         r  s.shift    l.shift       C.b       CCC       CIS
## 1 10.55157 0.8705245 1.077005 0.08563874 0.9936211 0.8649715 0.7, 0.94

plot

conc_xy = data.frame(predict = pred, actual =all_data_spread$sev[-train]) %>% 
ggplot(aes(actual,predict))+
  geom_point(size =2, color = "gray")+
  geom_abline(intercept = 0, slope= 1, size = .81, color = "black", linetype = "dashed")+
  geom_smooth(method = "lm", 
              color = "red",
              size =.81, se =F,
              fullrange=T)+
  theme_minimal_grid()+
  labs(x = "Predicted Severity (%)",
       y = "Actual Severity (%)")+
  coord_equal(xlim = c(0,100),
              ylim = c(0,100))+
  xlim(0,100)


ggsave("figs/concordance.png", dpi = 600, height = 3.5, width = 4)
## `geom_smooth()` using formula 'y ~ x'

Late blight

pics<-list.files("./pics/01-potato_late_bligh")
# length(pics)
#indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")


box = data.frame()

for(i in 1:length(pics)){

EX.L1<-stack(paste("./pics/01-potato_late_bligh/",pics[i],sep = ""))
EX.L1<-aggregate(EX.L1, fact=4)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)

# EX1.Indices<- fieldIndex(mosaic = EX.L1,
#                          index = c("NGRDI","BGI","GLI", "SCI","HI", "SI"), 
#                          myIndex = c("(Red-Blue)/Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1, myIndex ="Red", cropValue=1, cropAbove=F, plot = F)

cut = mask(EX.L1, EX.L2$mask)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)


df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  mutate(gray = 0.299*Red+0.587*Green+0.114*Blue) %>% 
  gather(c(1:(3+length(index)),15), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  dplyr::summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[i])


box = box %>% 
  bind_rows(dff)}
length(unique(box$leaf))
write.table(box,"data/indexes_PLB.txt")
box = read.table("data/indexes_PLB.txt")

Load severity data

library(gsheet)
sev_data = gsheet2tbl("https://docs.google.com/spreadsheets/d/1QMYhoFU4V4ItkAXyM_qYW4ODt0MctX9UJeFckB8bMQc/edit?usp=sharing")
## Warning: Missing column names filled in: 'X9' [9]
# 
# sev_data %>% 
#   group_by(photo) %>% 
#   summarise(n())

length(unique(sev_data$photo))
## [1] 200
all_data_PI = box %>% 
  mutate(file = leaf) %>% 
  dplyr::select(-leaf) %>% 
  right_join(sev_data) #%>% 
## Joining, by = "file"
  # filter(sev>0) %>% 
  # mutate(sev = case_when(sev==0 ~0.001,
  #                        sev >0 ~sev))
summary(all_data_PI$sev)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00   37.24   49.47   47.63   63.78   92.38

Images

hist_sev_pi =  all_data_PI %>% 
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean) %>% 
  ggplot(aes(sev))+
  geom_histogram(color = "white", fill = "black", bins =20)+
  theme_minimal_hgrid(font_size = 10)+
  labs(x = "Severity (%)",
       y = "Frequency")+
  scale_x_continuous(limits = c(-5,105), breaks = seq(0,100,25))+
  # theme_void()+
  # coord_fixed()+
  theme(panel.background = element_rect(color = "black"),
        axis.title.y = element_text(size=8))
EX.L1<-stack(paste("./pics/01-potato_late_bligh/","PI21_2D.png",sep = ""))
EX.L1<-aggregate(EX.L1, fact=10)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)
## [1] "3 layers available"
EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)
## [1] "3 layers available"
EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Red"), cropValue=1, cropAbove=F, plot = F)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Red"
cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot = F)
## [1] "3 layers available"
# plot(EX.L4$HUE)
rgb_fig_pi = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_map()+
  coord_fixed()+
  xlim(250,1500)+
  ylim(50,1300)+
  theme(panel.background = element_rect(color = "white"))
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
gli_fig_pi = as.data.frame(EX.L4$BGI, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = BGI))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_map()+
  coord_fixed()+
  xlim(250,1500)+
  ylim(50,1300)+
  theme(panel.background = element_rect(color = "white"),
        legend.title = element_text(size = 8),
        legend.text = element_text(size = 8))

# rgb_fig_pi + gli_fig_pi
rgb_fig_sbr + gli_fig_sbr + hist_sev_sbr #+
## Warning: Removed 2 rows containing missing values (geom_bar).

#   rgb_fig_wlb + gli_fig_wlb + hist_sev_WLB+
#   rgb_fig_xy + gli_fig_xy +hist_sev_xy+
#   rgb_fig_pi + gli_fig_pi +hist_sev_pi+
#    plot_layout(widths = c(1, 1, 1),
#                heights = c(1,1,1,1))+
#   plot_annotation(tag_levels = 'A')

# ggsave("figs/leaf_gli.png",dpi = 600, height = 8, width =8)

Relationship sev indices

rgb_gg_pi = all_data_PI %>% 
  filter(index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev, color = index)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =1)+
  scale_color_manual(values = c("steelblue","darkgreen", "darkred"))+
  theme_minimal_hgrid()+
  labs(x = "Mean value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))+
  theme(legend.position = "none")
rgb_gg_pi
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

index_gg_pi = all_data_PI %>% 
  filter(!index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(color = "black", se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =2)+
  theme_minimal_hgrid()+
  labs(x = "Mean index value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))
index_gg_pi
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plot_grid(
  plot_grid(NULL,rgb_gg_pi,NULL, rel_widths =c(0.18,1,0.2), nrow = 1),
          index_gg_pi,
          nrow = 2,
          rel_heights = c(0.5,1))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggsave("figs/index_sev_pi.png", dpi = 500, height = 8, width = 10)
cor_PI = all_data_PI %>% 
  group_by(index) %>% 
  dplyr::summarise(cor = round(  cor.test(mean,sev, method = "spearman")$estimate,3),
                   P_value = round(cor.test(mean,sev, method = "spearman")$p.value,4)) %>% 
  arrange(-cor)
## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev, method = "spearman"): Cannot compute
## exact p-value with ties
## `summarise()` ungrouping output (override with `.groups` argument)
cor_PI
## # A tibble: 13 x 3
##    index    cor P_value
##    <chr>  <dbl>   <dbl>
##  1 BGI    0.762  0     
##  2 Blue   0.708  0     
##  3 BI     0.399  0     
##  4 gray   0.356  0     
##  5 Red    0.295  0     
##  6 Green  0.267  0.0001
##  7 SCI    0.106  0.136 
##  8 HUE    0.098  0.169 
##  9 VARI  -0.069  0.332 
## 10 NGRDI -0.106  0.136 
## 11 HI    -0.161  0.0224
## 12 GLI   -0.492  0     
## 13 SI    -0.724  0

Spread df

all_data_spread = all_data_PI %>% 
  pivot_wider(id_col = c(file,sev),
              names_from = index, 
              values_from =  mean)   

all_data_spread
## # A tibble: 200 x 15
##    file    sev    BGI    BI  Blue   GLI  gray Green     HI    HUE  NGRDI   Red
##    <chr> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl> <dbl>
##  1 foto~ 13.6  0.254   57.1 20.7  0.304  64.0  74.1  0.511 -0.663 0.0975  60.9
##  2 foto~ 11.8  0.227   54.3 18.0  0.311  60.8  70.3  0.550 -0.682 0.0919  58.6
##  3 foto~  0.95 0.0561  45.4  4.38 0.477  51.6  64.9  0.282 -0.658 0.209   43.4
##  4 foto~ 15.2  0.313   60.2 26.0  0.274  67.4  77.2  0.499 -0.665 0.0914  64.0
##  5 foto~  7.81 0.289   55.1 25.5  0.391  62.3  76.5 -0.194 -0.853 0.248   48.4
##  6 foto~  1.39 0.360   56.3 28.6  0.287  63.0  73.5  0.183 -0.783 0.138   55.5
##  7 foto~  2.08 0.318   52.9 25.0  0.313  59.2  69.6  0.146 -0.686 0.148   51.9
##  8 foto~  2.03 0.204   52.9 16.2  0.338  59.7  70.4  0.499 -0.660 0.118   55.3
##  9 foto~  0.6  0.199   51.7 15.5  0.336  58.2  68.3  0.507 -0.682 0.111   54.5
## 10 foto~  1.74 0.281   49.6 20.6  0.299  55.7  64.7  0.446 -0.620 0.110   51.4
## # ... with 190 more rows, and 3 more variables: SCI <dbl>, SI <dbl>, VARI <dbl>

GBM

train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.75*length(all_data_spread$sev),1))
# length(train)
gbm.fit = gbm(sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI,
             data = all_data_spread[train,],
             distribution = "gaussian",
              n.trees = 1000,
             interaction.depth = 3,
             shrinkage = 0.1,
             cv.folds = 5,
             n.cores = NULL, # will use all cores by default
             verbose = FALSE)
print(gbm.fit)
## gbm(formula = sev ~ BGI + BI + GLI + HI + HUE + NGRDI + VARI + 
##     gray + Red + Green + Blue + SI + SCI, distribution = "gaussian", 
##     data = all_data_spread[train, ], n.trees = 1000, interaction.depth = 3, 
##     shrinkage = 0.1, cv.folds = 5, verbose = FALSE, n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 1000 iterations were performed.
## The best cross-validation iteration was 80.
## There were 13 predictors of which 13 had non-zero influence.
sqrt(min(gbm.fit$cv.error))
## [1] 14.0629
gbm.perf(gbm.fit, method = "cv")

## [1] 80
# find index for n trees with minimum CV error
min_MSE <- which.min(gbm.fit$cv.error)
sqrt(gbm.fit$cv.error[min_MSE])
## [1] 14.0629
# best.iter <- gbm.perf(model1, method = "test")
# print(best.iter)

pred = predict(gbm.fit, newdata = all_data_spread[-train,-1], ntrees = 5000 )
## Using 80 trees...
sqrt(mean(((pred)-all_data_spread$sev[-train])^2))
## [1] 13.84988
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.7509533
plot((pred), (pred)-all_data_spread$sev[-train])
abline(a=0,b=0)

Testing various hyperparameters

Create hyperparameter grid

hyper_grid <- expand.grid(
  shrinkage = c(.001, .01, .1, .3),
  interaction.depth = c(1, 3, 5, 6),
  n.minobsinnode = c(5, 10, 15),
  bag.fraction = c(.5,.65, .8, 1), 
  optimal_trees = 0,               # a place to dump results
  min_RMSE = 0,
  CCC =0 # a place to dump results
)
# total number of combinations
nrow(hyper_grid)
## [1] 192
# randomize data
set.seed(123)
train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.80*length(all_data_spread$sev),1))

# grid search 
for(i in 1:nrow(hyper_grid)) {

# reproducibility
set.seed(123)


 # train model
gbm.tune <- gbm(
  formula = sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI, 
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = hyper_grid$interaction.depth[i],
  shrinkage = hyper_grid$shrinkage[i],
  n.minobsinnode = hyper_grid$n.minobsinnode[i],
  bag.fraction = hyper_grid$bag.fraction[i],
  train.fraction = .75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE)

pred = predict(gbm.tune, newdata = all_data_spread[-train,-1], ntrees = 5000 )
 # add min training error and trees to grid
  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$valid.error))
  hyper_grid$CCC[i] = CCC((pred), all_data_spread$sev[-train])$rho.c$est
  
}
## Using 4982 trees...
## Using 936 trees...
## Using 290 trees...
## Using 18 trees...
## Using 2198 trees...
## Using 215 trees...
## Using 26 trees...
## Using 6 trees...
## Using 2231 trees...
## Using 296 trees...
## Using 25 trees...
## Using 6 trees...
## Using 2231 trees...
## Using 329 trees...
## Using 30 trees...
## Using 6 trees...
## Using 4669 trees...
## Using 496 trees...
## Using 42 trees...
## Using 269 trees...
## Using 3338 trees...
## Using 307 trees...
## Using 30 trees...
## Using 9 trees...
## Using 3338 trees...
## Using 343 trees...
## Using 25 trees...
## 
## Using 25 trees...
## Using 3338 trees...
## Using 343 trees...
## Using 25 trees...
## 
## Using 25 trees...
## Using 4617 trees...
## Using 496 trees...
## Using 47 trees...
## Using 24 trees...
## Using 4601 trees...
## Using 3363 trees...
## Using 52 trees...
## Using 147 trees...
## Using 4601 trees...
## Using 3363 trees...
## Using 52 trees...
## Using 147 trees...
## Using 4601 trees...
## Using 3363 trees...
## Using 52 trees...
## Using 147 trees...
## Using 4991 trees...
## Using 936 trees...
## Using 83 trees...
## Using 23 trees...
## Using 2283 trees...
## Using 275 trees...
## Using 29 trees...
## Using 6 trees...
## Using 2181 trees...
## Using 206 trees...
## Using 23 trees...
## Using 6 trees...
## Using 2200 trees...
## Using 210 trees...
## Using 23 trees...
## Using 6 trees...
## Using 4996 trees...
## Using 725 trees...
## Using 82 trees...
## Using 50 trees...
## Using 2792 trees...
## Using 269 trees...
## Using 21 trees...
## Using 9 trees...
## Using 2781 trees...
## Using 298 trees...
## Using 74 trees...
## Using 51 trees...
## Using 2781 trees...
## Using 277 trees...
## Using 21 trees...
## Using 9 trees...
## Using 4661 trees...
## Using 495 trees...
## Using 50 trees...
## Using 10 trees...
## Using 4437 trees...
## Using 367 trees...
## Using 50 trees...
## Using 10 trees...
## Using 4246 trees...
## Using 356 trees...
## Using 52 trees...
## Using 10 trees...
## Using 4246 trees...
## Using 356 trees...
## Using 52 trees...
## Using 10 trees...
## Using 4995 trees...
## Using 954 trees...
## Using 59 trees...
## Using 32 trees...
## Using 2542 trees...
## Using 264 trees...
## Using 22 trees...
## Using 7 trees...
## Using 2186 trees...
## Using 214 trees...
## Using 22 trees...
## Using 7 trees...
## Using 2047 trees...
## Using 250 trees...
## Using 22 trees...
## Using 5 trees...
## Using 4995 trees...
## Using 1195 trees...
## Using 251 trees...
## Using 32 trees...
## Using 2467 trees...
## Using 285 trees...
## Using 22 trees...
## Using 6 trees...
## Using 2663 trees...
## Using 238 trees...
## Using 22 trees...
## Using 6 trees...
## Using 2612 trees...
## Using 214 trees...
## Using 25 trees...
## Using 7 trees...
## Using 4995 trees...
## Using 689 trees...
## Using 71 trees...
## Using 22 trees...
## Using 3167 trees...
## Using 285 trees...
## Using 36 trees...
## Using 10 trees...
## Using 3846 trees...
## Using 344 trees...
## Using 35 trees...
## Using 9 trees...
## Using 3846 trees...
## Using 344 trees...
## Using 35 trees...
## Using 9 trees...
## Using 4006 trees...
## Using 3446 trees...
## Using 327 trees...
## Using 72 trees...
## Using 2391 trees...
## Using 237 trees...
## Using 31 trees...
## Using 7 trees...
## Using 2297 trees...
## Using 232 trees...
## Using 19 trees...
## Using 7 trees...
## Using 2519 trees...
## Using 219 trees...
## Using 26 trees...
## Using 6 trees...
## Using 5000 trees...
## Using 1416 trees...
## Using 139 trees...
## Using 31 trees...
## Using 3049 trees...
## Using 329 trees...
## Using 37 trees...
## Using 11 trees...
## Using 2371 trees...
## Using 236 trees...
## Using 24 trees...
## Using 7 trees...
## Using 2302 trees...
## Using 232 trees...
## Using 21 trees...
## Using 7 trees...
## Using 4999 trees...
## Using 3942 trees...
## Using 371 trees...
## Using 138 trees...
## Using 3041 trees...
## Using 312 trees...
## Using 23 trees...
## Using 8 trees...
## Using 3754 trees...
## Using 348 trees...
## Using 35 trees...
## Using 9 trees...
## Using 4014 trees...
## Using 405 trees...
## Using 35 trees...
## Using 10 trees...
best_par = hyper_grid %>% 
  dplyr::arrange(-CCC) %>%
  head(10)
best_par
##    shrinkage interaction.depth n.minobsinnode bag.fraction optimal_trees
## 1      0.300                 1             15         0.50            24
## 2      0.300                 3             15         0.65            10
## 3      0.300                 5             15         0.65            10
## 4      0.300                 6             15         0.65            10
## 5      0.300                 1             15         0.80            22
## 6      0.300                 1             15         1.00           138
## 7      0.010                 1             15         0.65           495
## 8      0.010                 1             15         0.80           689
## 9      0.001                 1             15         0.65          4661
## 10     0.001                 1             15         0.50          4617
##    min_RMSE       CCC
## 1  12.22198 0.7088796
## 2  11.82089 0.7009918
## 3  12.21880 0.7008317
## 4  12.21880 0.7008317
## 5  11.57058 0.6999291
## 6  12.01776 0.6954443
## 7  12.60668 0.6931396
## 8  12.49874 0.6891423
## 9  12.58996 0.6836161
## 10 12.76863 0.6821743
# gbm.tune$fit

Best model

# for reproducibility
set.seed(123)

# train GBM model
gbm.fit.final <- gbm(
  formula = sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI, 
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = best_par$optimal_trees[1],
  interaction.depth = best_par$interaction.depth[1],
  shrinkage = best_par$shrinkage[1],
  n.minobsinnode = best_par$n.minobsinnode[1],
  bag.fraction = best_par$bag.fraction[1], 
  train.fraction =0.75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE
  )

Relative influence

par(mar = c(5, 8, 1, 1))
summary_gbm_plb = summary(
  gbm.fit.final, 
  cBars = 13,
  method = relative.influence, # also can use permutation.test.gbm
  las = 2
  )

rel_plb = summary_gbm_plb  %>% 
  rownames_to_column("index") %>% 
  ggplot(aes(rel.inf, reorder(var, rel.inf)))+
  geom_col(aes(fill =rel.inf>1, color =rel.inf>1 ), width = 0.85)+
  theme_minimal_vgrid()+
  labs(x = "Relative influence (%)",
       y = "Model predictors",
       fill = "RI > 1%",
       color = "RI > 1%")
rel_plb

# ggsave("figs/var_influence.png",dpi = 600, height = 4, width = 6)

Partial dependence plots

gbm.fit.final %>%
  pdp::partial(pred.var = "BGI", n.trees = gbm.fit.final$n.trees, grid.resolution = 100) %>%
  ggplot(aes( BGI,(yhat)))+
  geom_line()

LIME

library(lime)
model_type.gbm <- function(x, ...) {
  return("regression")
}

predict_model.gbm <- function(x, newdata, ...) {
  pred <- predict(x, newdata, n.trees = x$n.trees)
  return(as.data.frame(pred))
}
# get a few observations to perform local interpretation on
local_obs <- (all_data_spread[-train,])[1:4, ]

# apply LIME
explainer <- lime(all_data_spread[train,], gbm.fit.final)
explanation <- lime::explain(local_obs, explainer, n_features = 7, n.trees =1)
plot_features(explanation)

Prediction

# predict values for test data
pred <- predict(gbm.fit.final, n.trees = gbm.fit.final$n.trees, all_data_spread[-train,])

# results
caret::RMSE(pred, all_data_spread[-train,]$sev)
## [1] 13.38866
CCC(pred, all_data_spread$sev[-train])$rho.c$est
## [1] 0.7088796
cor(pred, all_data_spread$sev[-train])^2
## [1] 0.5509299
accuracy_pi =data.frame(predi=pred, actual = all_data_spread$sev[-train]) %>% 
  summarise(RMSE = caret::RMSE(pred, actual),
            r = cor(pred, actual),
            s.shift = CCC(pred, actual)$s.shift,
            l.shift = CCC(pred, actual)$l.shift,
            C.b = CCC(pred, actual)$C.b,
            CCC = CCC(pred, actual)$rho.c$est,
            CIS = paste(
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[2],2),","," ",
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[3],2),sep = ""
  ))
accuracy_pi
##       RMSE         r  s.shift    l.shift       C.b       CCC        CIS
## 1 13.38866 0.7422465 1.285102 -0.1757541 0.9550461 0.7088796 0.53, 0.83

plot

conc_pi = data.frame(predict = pred, actual =all_data_spread$sev[-train]) %>% 
ggplot(aes(actual,predict))+
  geom_point(size =2, color = "gray")+
  geom_abline(intercept = 0, slope= 1, size = .81, color = "black", linetype = "dashed")+
  geom_smooth(method = "lm", 
              color = "red",
              size =.81, se =F,
              fullrange=T)+
  theme_minimal_grid()+
  labs(x = "Predicted Severity (%)",
       y = "Actual Severity (%)")+
  coord_equal(xlim = c(0,100),
              ylim = c(0,100))+
  xlim(0,100)


ggsave("figs/concordance.png", dpi = 600, height = 3.5, width = 4)
## `geom_smooth()` using formula 'y ~ x'

Calonectria leaf blight

pics<-list.files("./pics/01-Calonectria_leaf_bligth")
# length(pics)
#indices
index = c("BI","SCI","GLI","HI","SI","VARI","HUE","BGI","NGRDI")


box = data.frame()

for(i in 1:length(pics)){

EX.L1<-stack(paste("./pics/01-Calonectria_leaf_bligth/",pics[i],sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)

EX1.Indices<- fieldIndex(mosaic = EX.L1,
                         index = index, 
                         myIndex = c("Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=175, cropAbove=T, plot = F)

cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)


df = as(EX.L4, "SpatialPixelsDataFrame")
dff = as.data.frame(df) %>% 
  mutate(gray = 0.299*Red+0.587*Green+0.114*Blue) %>% 
  gather(c(1:(3+length(index)),15), key = "index", value = "value" ) %>%
  filter(!is.na(value),
         !is.infinite(value)) %>% 
  group_by(index) %>% 
  dplyr::summarise(mean = mean(value, na.rm = T),
            std = sd(value),
            Q25 = quantile(value,0.25),
            Q50 = quantile(value,0.50),
            Q75 = quantile(value,0.75)) %>% 
  mutate(leaf = pics[i])


box = box %>% 
  bind_rows(dff)}
length(unique(box$leaf))
write.table(box,"data/indexes_calonec.txt")
box = read.table("data/indexes_calonec.txt")
data_calo_load = gsheet2tbl("https://docs.google.com/spreadsheets/d/1Nqd9NqbynjR1bI2wrYdsKXZT3HACT8CVqyfY5n70DhI/edit?usp=sharing") %>% 
  mutate(file = as.character(file)) %>% 
  dplyr::select(file,area_total,area_doente_roxa,area_doente,sev_roxa,sev)
head(data_calo_load)
## # A tibble: 6 x 6
##   file  area_total area_doente_roxa area_doente sev_roxa   sev
##   <chr>      <dbl>            <dbl>       <dbl>    <dbl> <dbl>
## 1 1         411776            54374        9384     13.2  2.28
## 2 2         415627            81757       55557     19.7 13.4 
## 3 3         761523           569173      413002     74.7 54.2 
## 4 4         798787           708346      594451     88.7 74.4 
## 5 5         657200           219361       85449     33.4 13.0 
## 6 6         784817           628389      628389     80.1 80.1
data_calo = box %>% 
  separate(leaf, into=c("file","format"), sep =".jpg") %>% 
  dplyr::select(-format) %>% 
  full_join(data_calo_load, by="file") %>% 
  mutate(sev=sev_roxa)
# data_calo

length(unique(data_calo$sev))
## [1] 300
summary(data_calo$sev)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.8715  4.4431  9.8264 16.2402 20.1989 95.4470

Images

hist_sev_calo =  data_calo %>% 
  pivot_wider(id_col = c(file,sev_roxa),
              names_from = index, 
              values_from =  mean) %>%
  ggplot(aes(sev_roxa))+
  geom_histogram(color = "white", fill = "black", bins = 20)+
  theme_minimal_hgrid(font_size = 10)+
  labs(x = "Severity (%)",
       y = "Frequency")+
  scale_x_continuous(limits = c(-5,105), breaks = seq(0,100,25))+
  # theme_void()+
  # coord_fixed()+
  theme(panel.background = element_rect(color = "black"),
        axis.title.y = element_text(size=8))
EX.L1<-stack(paste("./pics/01-Calonectria_leaf_bligth/","57.jpg",sep = ""))
EX.L1<-aggregate(EX.L1, fact=7)
EX.L.Shape<-fieldPolygon(mosaic=EX.L1, extent=T, plot = F)
## [1] "3 layers available"
# EX1.Indices<- fieldIndex(mosaic = EX.L1,
#                          index = index, 
#                          myIndex = c("Green"), plot = F)

EX.L2<-fieldMask(mosaic=EX.L1,  myIndex = c("Blue"), cropValue=175, cropAbove=T, plot = F)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
cut = mask(EX.L1, EX.L2$newMosaic)
EX.L4<-fieldIndex(mosaic=cut,
                  index =index,
                  plot =F)
## [1] "3 layers available"
# plot(EX.L4$HUE)
rgb_fig_calo = RStoolbox::ggRGB(EX.L2$newMosaic,
                 r = 1,
                 g = 2,
                 b = 3)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"))
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
gli_fig_calo = as.data.frame(EX.L4$HUE, xy=TRUE, na.rm =T) %>% 
  ggplot(aes(x, y, fill = HUE))+
  geom_tile()+
  scale_fill_viridis_c(option = "B",direction = -1)+
  theme_map()+
  coord_fixed()+
  theme(panel.background = element_rect(color = "white"),
        legend.title = element_text(size = 8),
        legend.text = element_text(size = 8))

rgb_fig_calo+ gli_fig_calo

rgb_fig_sbr + gli_fig_sbr + hist_sev_sbr +
  rgb_fig_xy + gli_fig_xy +hist_sev_xy+
  rgb_fig_calo + gli_fig_calo + hist_sev_calo+
  rgb_fig_wlb + gli_fig_wlb + hist_sev_WLB+
  rgb_fig_pi + gli_fig_pi + hist_sev_pi+
   plot_layout(widths = c(1, 1, 1),
               heights = c(1,1,1,1,1))+
  plot_annotation(tag_levels = 'A')&
  theme(legend.key.size = unit(3, 'mm'),
        legend.text = element_text(size =6))
## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

ggsave("figs/leaf_gli.png",dpi = 600, height = 9, width =7)
## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

Relationship sev indices

 rgb_gg_calo =  data_calo %>% 
  filter(index %in% c("Red", "Blue", "Green")) %>%
    ggplot(aes(mean, sev_roxa, color = index)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =1)+
  scale_color_manual(values = c("steelblue","darkgreen", "darkred"))+
  theme_minimal_hgrid()+
  labs(x = "Mean value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))+
  theme(legend.position = "none")
rgb_gg_calo
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

index_gg_calo = data_calo %>% 
  filter(!index %in% c("Red", "Blue", "Green")) %>% 
    ggplot(aes(mean, sev_roxa, label = file)) + 
  # geom_text()+
  geom_point(color = "gray", size  =3)+
  geom_smooth(color = "black", se = F, size = 2)+
  facet_wrap(~index, scales = "free_x", nrow =2)+
  theme_minimal_hgrid()+
  labs(x = "Mean index value in the image",
       y = "Disease severity (%)")+
  theme(panel.border = element_rect(color = "gray"))
index_gg_calo
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plot_grid(
  plot_grid(NULL,rgb_gg_calo,NULL, rel_widths =c(0.18,1,0.2), nrow = 1),
          index_gg_calo,
          nrow = 2,
          rel_heights = c(0.5,1))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggsave("figs/index_sev_calo.png", dpi = 500, height = 8, width = 10)
cor_calo = data_calo %>% 
  group_by(index) %>% 
  dplyr::summarise(cor = round(  cor.test(mean,sev_roxa, method = "spearman")$estimate,3),
                   P_value = round(cor.test(mean,sev_roxa, method = "spearman")$p.value,4)) %>% 
  arrange(-cor)
## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties

## Warning in cor.test.default(mean, sev_roxa, method = "spearman"): Cannot compute
## exact p-value with ties
## `summarise()` ungrouping output (override with `.groups` argument)
cor_calo
## # A tibble: 13 x 3
##    index    cor P_value
##    <chr>  <dbl>   <dbl>
##  1 HUE    0.982   0    
##  2 SCI    0.773   0    
##  3 Red    0.754   0    
##  4 SI     0.678   0    
##  5 HI     0.621   0    
##  6 BI     0.568   0    
##  7 gray   0.479   0    
##  8 BGI    0.405   0    
##  9 Blue   0.36    0    
## 10 Green  0.065   0.264
## 11 GLI   -0.736   0    
## 12 VARI  -0.743   0    
## 13 NGRDI -0.773   0

Spread df

all_data_spread = data_calo %>% 
  pivot_wider(id_col = c(file,sev_roxa),
              names_from = index, 
              values_from =  mean) %>% 
  mutate(sev = sev_roxa) %>% 
  dplyr::select(-sev_roxa)

all_data_spread
## # A tibble: 300 x 15
##    file    BGI    BI  Blue     GLI  gray Green     HI    HUE   NGRDI   Red
##    <chr> <dbl> <dbl> <dbl>   <dbl> <dbl> <dbl>  <dbl>  <dbl>   <dbl> <dbl>
##  1 1     0.688  87.8  75.2 0.225    93.8  111. -0.985 -1.21   0.265   66.6
##  2 10    0.733 152.  109.  0.00994 155.   149.  2.75   1.30  -0.101  185. 
##  3 100   0.678  95.3  82.5 0.231   102.   122. -1.04  -1.36   0.274   71.5
##  4 101   0.661  97.5  79.9 0.204   105.   122. -0.490 -1.27   0.203   82.7
##  5 102   0.631  87.3  71.9 0.257    94.6  114. -1.05  -1.35   0.291   65.1
##  6 103   0.599  90.4  69.1 0.243    98.7  117. -0.516 -1.23   0.233   74.2
##  7 104   0.573  89.2  69.9 0.307    97.8  122. -1.11  -1.45   0.344   61.3
##  8 105   0.768  92.9  77.9 0.0973   97.0  103.  1.29  -0.417  0.0721  92.9
##  9 106   0.645 102.   79.6 0.187   110.   124.  0.765 -1.01   0.161   93.1
## 10 107   0.660  88.9  76.0 0.241    96.1  115. -1.40  -1.45   0.279   66.6
## # ... with 290 more rows, and 4 more variables: SCI <dbl>, SI <dbl>,
## #   VARI <dbl>, sev <dbl>

GBM

train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.75*length(all_data_spread$sev),1))
# length(train)
gbm.fit = gbm(sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI,
             data = all_data_spread[train,],
             distribution = "gaussian",
              n.trees = 1000,
             interaction.depth = 3,
             shrinkage = 0.1,
             cv.folds = 5,
             n.cores = NULL, # will use all cores by default
             verbose = FALSE)
print(gbm.fit)
## gbm(formula = sev ~ BGI + BI + GLI + HI + HUE + NGRDI + VARI + 
##     gray + Red + Green + Blue + SI + SCI, distribution = "gaussian", 
##     data = all_data_spread[train, ], n.trees = 1000, interaction.depth = 3, 
##     shrinkage = 0.1, cv.folds = 5, verbose = FALSE, n.cores = NULL)
## A gradient boosted model with gaussian loss function.
## 1000 iterations were performed.
## The best cross-validation iteration was 185.
## There were 13 predictors of which 13 had non-zero influence.
sqrt(min(gbm.fit$cv.error))
## [1] 4.651259
gbm.perf(gbm.fit, method = "cv")

## [1] 185
# find index for n trees with minimum CV error
min_MSE <- which.min(gbm.fit$cv.error)
sqrt(gbm.fit$cv.error[min_MSE])
## [1] 4.651259
# best.iter <- gbm.perf(model1, method = "test")
# print(best.iter)

pred = predict(gbm.fit, newdata = all_data_spread[-train,-1], ntrees = 5000 )
## Using 185 trees...
sqrt(mean(((pred)-all_data_spread$sev[-train])^2))
## [1] 4.170014
CCC((pred), all_data_spread$sev[-train])$rho.c$est
## [1] 0.9735623
plot((pred), (pred)-all_data_spread$sev[-train])
abline(a=0,b=0)

Testing various hyperparameters

Create hyperparameter grid

hyper_grid <- expand.grid(
  shrinkage = c(.001, .01, .1, .3),
  interaction.depth = c(1, 3, 5, 6),
  n.minobsinnode = c(5, 10, 15),
  bag.fraction = c(.5,.65, .8, 1), 
  optimal_trees = 0,               # a place to dump results
  min_RMSE = 0,
  CCC =0 # a place to dump results
)
# total number of combinations
nrow(hyper_grid)
## [1] 192
# randomize data
set.seed(1234)
train=sample(x = 1:length(all_data_spread$sev), 
             size = round(0.80*length(all_data_spread$sev),1))

# grid search 
for(i in 1:nrow(hyper_grid)) {

# reproducibility
set.seed(123)


 # train model
gbm.tune <- gbm(
  formula = sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI, 
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = 5000,
  interaction.depth = hyper_grid$interaction.depth[i],
  shrinkage = hyper_grid$shrinkage[i],
  n.minobsinnode = hyper_grid$n.minobsinnode[i],
  bag.fraction = hyper_grid$bag.fraction[i],
  train.fraction = .75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE)

pred = predict(gbm.tune, newdata = all_data_spread[-train,-1], ntrees = 5000 )
 # add min training error and trees to grid
  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$valid.error)
  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$valid.error))
  hyper_grid$CCC[i] = CCC((pred), all_data_spread$sev[-train])$rho.c$est
  
}
## Using 5000 trees...
## Using 4835 trees...
## Using 555 trees...
## Using 104 trees...
## Using 5000 trees...
## Using 4997 trees...
## Using 1871 trees...
## Using 4957 trees...
## Using 5000 trees...
## Using 4957 trees...
## Using 1689 trees...
## Using 1683 trees...
## Using 5000 trees...
## Using 4987 trees...
## Using 1968 trees...
## Using 12 trees...
## Using 4996 trees...
## Using 5000 trees...
## Using 546 trees...
## Using 42 trees...
## Using 4996 trees...
## Using 1376 trees...
## Using 115 trees...
## Using 40 trees...
## Using 4996 trees...
## Using 1377 trees...
## Using 56 trees...
## Using 24 trees...
## Using 4996 trees...
## Using 1376 trees...
## Using 58 trees...
## Using 4114 trees...
## Using 4293 trees...
## Using 1642 trees...
## Using 201 trees...
## Using 81 trees...
## Using 4996 trees...
## Using 661 trees...
## Using 47 trees...
## Using 42 trees...
## Using 4996 trees...
## Using 863 trees...
## Using 47 trees...
## Using 31 trees...
## Using 4996 trees...
## Using 863 trees...
## Using 47 trees...
## Using 31 trees...
## Using 5000 trees...
## Using 4837 trees...
## Using 395 trees...
## Using 114 trees...
## Using 5000 trees...
## Using 2697 trees...
## Using 253 trees...
## Using 394 trees...
## Using 4998 trees...
## Using 2692 trees...
## Using 175 trees...
## Using 4982 trees...
## Using 4998 trees...
## Using 3721 trees...
## Using 456 trees...
## Using 244 trees...
## Using 5000 trees...
## Using 3831 trees...
## Using 461 trees...
## Using 97 trees...
## Using 5000 trees...
## Using 1073 trees...
## Using 115 trees...
## Using 4999 trees...
## Using 5000 trees...
## Using 712 trees...
## Using 115 trees...
## Using 35 trees...
## Using 5000 trees...
## Using 706 trees...
## Using 115 trees...
## Using 37 trees...
## Using 4974 trees...
## Using 1640 trees...
## Using 147 trees...
## Using 96 trees...
## Using 5000 trees...
## Using 822 trees...
## Using 46 trees...
## Using 30 trees...
## Using 5000 trees...
## Using 955 trees...
## Using 46 trees...
## Using 37 trees...
## Using 5000 trees...
## Using 955 trees...
## Using 46 trees...
## Using 30 trees...
## Using 5000 trees...
## Using 3047 trees...
## Using 379 trees...
## Using 62 trees...
## Using 4998 trees...
## Using 1315 trees...
## Using 253 trees...
## Using 105 trees...
## Using 4998 trees...
## Using 1611 trees...
## Using 132 trees...
## Using 26 trees...
## Using 4998 trees...
## Using 4957 trees...
## Using 128 trees...
## Using 26 trees...
## Using 5000 trees...
## Using 4828 trees...
## Using 1231 trees...
## Using 1735 trees...
## Using 5000 trees...
## Using 2842 trees...
## Using 3829 trees...
## Using 14 trees...
## Using 5000 trees...
## Using 525 trees...
## Using 79 trees...
## Using 29 trees...
## Using 5000 trees...
## Using 539 trees...
## Using 55 trees...
## Using 23 trees...
## Using 4999 trees...
## Using 4606 trees...
## Using 331 trees...
## Using 160 trees...
## Using 5000 trees...
## Using 1046 trees...
## Using 85 trees...
## Using 34 trees...
## Using 5000 trees...
## Using 870 trees...
## Using 89 trees...
## Using 38 trees...
## Using 5000 trees...
## Using 870 trees...
## Using 85 trees...
## Using 31 trees...
## Using 5000 trees...
## Using 4991 trees...
## Using 843 trees...
## Using 262 trees...
## Using 5000 trees...
## Using 3072 trees...
## Using 213 trees...
## Using 53 trees...
## Using 5000 trees...
## Using 1799 trees...
## Using 242 trees...
## Using 51 trees...
## Using 5000 trees...
## Using 2183 trees...
## Using 2385 trees...
## Using 44 trees...
## Using 5000 trees...
## Using 4104 trees...
## Using 582 trees...
## Using 1097 trees...
## Using 5000 trees...
## Using 588 trees...
## Using 63 trees...
## Using 11 trees...
## Using 4999 trees...
## Using 548 trees...
## Using 52 trees...
## Using 15 trees...
## Using 5000 trees...
## Using 584 trees...
## Using 58 trees...
## Using 14 trees...
## Using 5000 trees...
## Using 1121 trees...
## Using 133 trees...
## Using 156 trees...
## Using 3806 trees...
## Using 382 trees...
## Using 42 trees...
## Using 11 trees...
## Using 3959 trees...
## Using 400 trees...
## Using 41 trees...
## Using 12 trees...
## Using 3830 trees...
## Using 394 trees...
## Using 37 trees...
## Using 12 trees...
best_par = hyper_grid %>% 
  dplyr::arrange(-CCC) %>%
  head(10)
best_par
##    shrinkage interaction.depth n.minobsinnode bag.fraction optimal_trees
## 1      0.300                 3              5            1            53
## 2      0.100                 1              5            1           843
## 3      0.010                 1              5            1          4991
## 4      0.300                 1              5            1           262
## 5      0.100                 3              5            1           213
## 6      0.001                 5              5            1          5000
## 7      0.001                 6              5            1          5000
## 8      0.300                 6              5            1            44
## 9      0.300                 5              5            1            51
## 10     0.001                 3              5            1          5000
##    min_RMSE       CCC
## 1  3.188960 0.9921566
## 2  2.913543 0.9917062
## 3  3.008064 0.9912300
## 4  3.429057 0.9907054
## 5  2.960664 0.9906812
## 6  3.378191 0.9904229
## 7  3.403406 0.9903718
## 8  3.064615 0.9901287
## 9  3.177959 0.9900388
## 10 3.297901 0.9900336
# gbm.tune$fit

Best model

# for reproducibility
set.seed(123)

# train GBM model
gbm.fit.final <- gbm(
  formula = sev ~BGI+BI+GLI+HI+HUE+NGRDI+VARI+gray+ Red+Green+Blue  + SI + SCI, 
  data = all_data_spread[train,],
  distribution = "gaussian",
  n.trees = best_par$optimal_trees[1],
  interaction.depth = best_par$interaction.depth[1],
  shrinkage = best_par$shrinkage[1],
  n.minobsinnode = best_par$n.minobsinnode[1],
  bag.fraction = best_par$bag.fraction[1], 
  train.fraction =0.75,
  n.cores = NULL, # will use all cores by default
  verbose = FALSE
  )

Relative influence

par(mar = c(5, 8, 1, 1))
summary_gbm_calo = summary(
  gbm.fit.final, 
  cBars = 13,
  method = relative.influence, # also can use permutation.test.gbm
  las = 2
  )

rel_calo = summary_gbm_calo %>% 
  rownames_to_column("index") %>% 
  ggplot(aes(rel.inf, reorder(var, rel.inf)))+
  geom_col(aes(fill =rel.inf>1, color =rel.inf>1 ), width = 0.85)+
  theme_minimal_vgrid()+
  labs(x = "Relative influence (%)",
       y = "Model predictors",
       fill = "RI > 1%",
       color = "RI > 1%")
rel_calo

# ggsave("figs/var_influence.png",dpi = 600, height = 4, width = 6)

Partial dependence plots

gbm.fit.final %>%
  pdp::partial(pred.var = "HUE", n.trees = gbm.fit.final$n.trees, grid.resolution = 100) %>%
  ggplot(aes( HUE,(yhat)))+
  geom_line()

LIME

library(lime)
model_type.gbm <- function(x, ...) {
  return("regression")
}

predict_model.gbm <- function(x, newdata, ...) {
  pred <- predict(x, newdata, n.trees = x$n.trees)
  return(as.data.frame(pred))
}
# get a few observations to perform local interpretation on
local_obs <- (all_data_spread[-train,])[1:4, ]

# apply LIME
explainer <- lime(all_data_spread[train,], gbm.fit.final)
explanation <- lime::explain(local_obs, explainer, n_features = 7, n.trees =1)
plot_features(explanation)

Prediction

# predict values for test data
pred <- predict(gbm.fit.final, n.trees = gbm.fit.final$n.trees, all_data_spread[-train,])

# results
caret::RMSE(pred, all_data_spread[-train,]$sev)
## [1] 2.358233
CCC(pred, all_data_spread$sev[-train])$rho.c$est
## [1] 0.9921566
cor(pred, all_data_spread$sev[-train])^2
## [1] 0.9872815
accuracy_calo = data.frame(predi=pred, actual = all_data_spread$sev[-train]) %>% 
  summarise(RMSE = caret::RMSE(pred, actual),
            r = cor(pred, actual),
            s.shift = CCC(pred, actual)$s.shift,
            l.shift = CCC(pred, actual)$l.shift,
            C.b = CCC(pred, actual)$C.b,
            CCC = CCC(pred, actual)$rho.c$est,
            CIS = paste(
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[2],2),","," ",
  round(CCC(pred, all_data_spread$sev[-train])$rho.c[3],2),sep = ""
  ))
accuracy_calo
##       RMSE         r  s.shift    l.shift       C.b       CCC     CIS
## 1 2.358233 0.9936204 1.047502 0.02822577 0.9985268 0.9921566 0.99, 1

plot

conc_calo = data.frame(predict = pred, actual =all_data_spread$sev[-train]) %>% 
ggplot(aes(actual,predict))+
  geom_point(size =2, color = "gray")+
  geom_abline(intercept = 0, slope= 1, size = .81, color = "black", linetype = "dashed")+
  geom_smooth(method = "lm", 
              color = "red",
              size =.81, se =F,
              fullrange=T)+
  theme_minimal_grid()+
  labs(x = "Predicted Severity (%)",
       y = "Actual Severity (%)")+
  coord_equal(xlim = c(0,100),
              ylim = c(0,100))+
  xlim(0,100)


ggsave("figs/concordance.png", dpi = 600, height = 3.5, width = 4)
## `geom_smooth()` using formula 'y ~ x'

Correlation

ind_order = c("Red","Green","Blue","BI","SCI","GLI","HI","NGRDI","SI","VARI","HUE","BGI","gray")
bind_rows(
cor_sbr %>% mutate(disease="SBR"),
cor_calo %>% mutate(disease="CLB"),
cor_xy %>% mutate(disease="NtXf"),
cor_wlb %>% mutate(disease="WLB"),
cor_PI %>% mutate(disease="PLB")) %>% 
  mutate(sig = case_when(P_value <0.05 ~ " ",
                         P_value >0.05 ~ "P>0.05")) %>% 
  mutate(disease = factor(disease, levels = c("PLB", "WLB","NtXf","CLB", "SBR")),
         index = factor(index, levels = ind_order)) %>% 
  ggplot(aes(index,disease, fill = cor, label = round(cor,3)))+
  geom_tile()+
  geom_text(size =3.5)+
  geom_point(aes(index,disease, color = sig), shape = "X", size =8, alpha = 0.6)+
  # scale_fill_gradient2(low = "darkred", mid = NA, high = "darkgreen")+
  scale_fill_distiller(palette = "RdBu", direction = 1)+
  scale_color_manual(values = c(NA,"black"))+
  theme_half_open()+
  labs(x = "",
       y = "", 
       fill = "  r",
       color ="")
## Warning: Removed 59 rows containing missing values (geom_point).

ggsave("figs/corr.png",dpi = 600, height = 3.5, width =10)
## Warning: Removed 59 rows containing missing values (geom_point).

Relative influence combo

summary_gbm_sbr
##         var     rel.inf
## HUE     HUE 87.88801884
## NGRDI NGRDI  6.28297306
## SCI     SCI  4.37465525
## GLI     GLI  0.47741094
## HI       HI  0.39728015
## VARI   VARI  0.15791219
## Red     Red  0.15652889
## BI       BI  0.11433955
## Blue   Blue  0.06497336
## Green Green  0.03215579
## SI       SI  0.02229384
## BGI     BGI  0.02060409
## gray   gray  0.01085406
summary_gbm_calo
##         var     rel.inf
## HUE     HUE 94.03402438
## SCI     SCI  4.09247026
## BI       BI  0.81359184
## BGI     BGI  0.28727216
## SI       SI  0.18018170
## NGRDI NGRDI  0.14039540
## Blue   Blue  0.13733611
## HI       HI  0.09923759
## gray   gray  0.06551079
## Green Green  0.05420577
## GLI     GLI  0.04420588
## Red     Red  0.03073479
## VARI   VARI  0.02083332
summary_gbm_xy
##         var    rel.inf
## HUE     HUE 45.0933820
## HI       HI 19.2008467
## SI       SI 16.0327582
## BGI     BGI  7.1783997
## Green Green  5.0459348
## NGRDI NGRDI  3.7484209
## BI       BI  2.1717994
## GLI     GLI  0.7792653
## Red     Red  0.7491929
## VARI   VARI  0.0000000
## Blue   Blue  0.0000000
## gray   gray  0.0000000
## SCI     SCI  0.0000000
summary_gbm_wlb
##         var    rel.inf
## VARI   VARI 28.4651011
## HI       HI 22.7166812
## Blue   Blue 17.7541396
## GLI     GLI 10.8559511
## SCI     SCI  6.9322339
## HUE     HUE  4.4167122
## NGRDI NGRDI  4.1782350
## BGI     BGI  1.4914608
## SI       SI  1.3595593
## Red     Red  0.8233217
## BI       BI  0.4903142
## Green Green  0.2792345
## gray   gray  0.2370553
summary_gbm_plb
##         var   rel.inf
## SI       SI 34.172257
## BGI     BGI 23.132425
## HUE     HUE 12.898477
## Green Green  9.907507
## Blue   Blue  9.040377
## BI       BI  3.744766
## GLI     GLI  2.959053
## HI       HI  2.437804
## gray   gray  1.707335
## NGRDI NGRDI  0.000000
## VARI   VARI  0.000000
## Red     Red  0.000000
## SCI     SCI  0.000000
rel_sbr + labs(title = paste("Soybean rust"))+
  rel_calo +labs(title = paste("Calonectria leaf blight"))+
  rel_wlb +labs(title = paste("Wheat leaf blast"))+
  rel_xy +labs(title = expression(bolditalic("N. tabacum-X. fastidiosa")))+
  rel_plb +labs(title = paste("Potato late blight"))+guide_area()+
  plot_layout(ncol =3, guides = "collect")+
  plot_annotation(tag_levels = 'A')&
  theme_minimal_grid(font_size = 9)&
  theme(plot.title = element_text(size =8))&
  xlim(0,100)

ggsave("figs/relative_influence_combo.png", dpi = 300, height = 5, width = 6)

Agreement

 conc_sbr+labs(title = paste("Soybean rust"),
               subtitle = paste("RMSE = ",round(accuracy_sbr$RMSE,2),", ",
                                "CCC = ",round(accuracy_sbr$CCC,3)))+
  conc_calo+labs(title = paste("Calonectria leaf blight"),
               subtitle = paste("RMSE = ",round(accuracy_calo$RMSE,2),", ",
                                "CCC = ",round(accuracy_calo$CCC,3)))+
  conc_wlb+labs(title = paste("Wheat leaf blast"),
               subtitle = paste("RMSE = ",round(accuracy_wlb$RMSE,2),", ",
                                "CCC = ",round(accuracy_wlb$CCC,3)))+
  conc_xy+labs(title = expression(bolditalic("N. tabacum-X. fastidiosa")),
               subtitle = paste("RMSE = ",round(accuracy_xy$RMSE,2),", ",
                                "CCC = ",round(accuracy_xy$CCC,3)))+
  conc_pi+labs(title = paste("Potato late blight"),
               subtitle = paste("RMSE = ",round(accuracy_pi$RMSE,2),", ",
                                "CCC = ",round(accuracy_pi$CCC,3)))+
  
  
   plot_layout(ncol = 3,
               widths = c(1, 1,1),
               heights = c(1,1))+

  plot_annotation(tag_levels = 'A')&
    theme_minimal_grid(font_size = 10)&
  theme(plot.title = element_text(size =10, face ="bold"),
      plot.subtitle = element_text(size =10, face = "plain"))
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

ggsave("figs/concordance.png", dpi = 600, height = 6, width = 8)
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

RGB bands by leaf

`

density_rgb = function(file_dir, limiar, index_cut, cropAbove=T,
                       left = 0.5,  bottom = 0.5,  right=1.1,  top=1.1){
  SBR_low_EX.L1<-stack(paste(file_dir))
SBR_low_EX.L1<-aggregate(SBR_low_EX.L1, fact=5)

SBR_low_EX.L2<-fieldMask(mosaic=SBR_low_EX.L1,  myIndex = c(index_cut), cropValue=limiar, cropAbove=cropAbove, plot = F)

cut = mask(SBR_low_EX.L1, SBR_low_EX.L2$newMosaic)
SBR_low_EX.L4<-fieldIndex(mosaic=cut,
                  # index =index,
                  plot =F)


SBR_low = RStoolbox::ggRGB(SBR_low_EX.L2$newMosaic,r = 1,g = 2,b = 3)+
  theme_map()+coord_fixed()+
  theme(panel.background = element_rect(color = NA, fill = NA),
        )

RLB_low_comb = data.frame(R = as.data.frame(SBR_low_EX.L4$Red),
           G = as.data.frame(SBR_low_EX.L4$Blue),
           B = as.data.frame(SBR_low_EX.L4$Green)) %>%
  na.omit() %>% 
  pivot_longer(1:3,names_to = "band", values_to = "value") %>% 
  # ggplot(aes(value, fill = band))+
  # geom_density(color = NA, alpha = 0.8)+
  
  ggplot(aes(value))+
  stat_slab(aes(fill = band), alpha = 0.6)+
   stat_pointinterval(aes(color = band),
                      position = position_dodge(width = .6, preserve = "single"),
                     # color = "gray40",
                     .width = c(0,0.95))+
  
  scale_fill_manual(values = c("blue", "green","red" ))+
  scale_color_manual(values = c("blue", "green","red" ))+
  scale_x_continuous(breaks = seq(0,250,50), limits = c(0,300))+
  theme_minimal()+
  theme(axis.text.y = element_blank(),
        panel.grid = element_blank(),
        axis.ticks.x = element_line(color = "gray"),
        axis.line.x = element_line(color = "gray"))+
  labs(x = "Pixel intensity",
       y = "",
       fill ="")+  
  guides(color =F)+
  inset_element(SBR_low, left,  bottom,  right, top, align_to = 'full')

RLB_low_comb$patches$layout$widths  <- 1
RLB_low_comb$patches$layout$heights <- 1
RLB_low_comb
}

SBR

SBR_low = density_rgb("./pics/01-soybean-rust-bg-blue/Ferrugem 52_Median.jpg",
                      limiar = 100, index_cut = "Blue",
                      left =0.55,bottom = 0.55,right = 1.1,top = 1.1)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
SBR_high = density_rgb("./pics/01-soybean-rust-bg-blue/Ferrugem 49_Median.jpg",
                       limiar = 100, index_cut = "Blue",
                      left =0.55,bottom = 0.55,right = 1.1,top = 1.1)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
SBR_low+SBR_high

Calo

calo_low = density_rgb("./pics/01-Calonectria_leaf_bligth/108.jpg",
                       limiar = 175, index_cut = "Blue",
                      left =0.5,bottom = 0.5,right = 1.2,top = 1.2)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
calo_high = density_rgb("./pics/01-Calonectria_leaf_bligth/153.jpg",
                       limiar = 175, index_cut = "Blue",
                      left =0.5,bottom = 0.5,right = 1.2,top = 1.2)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
calo_low+calo_high

## XY

xy_low = density_rgb("./pics/01-Xylella-tobacco-bg-white/68.jpg",
                       limiar = 200, index_cut = "Blue",
                      left =0.5,bottom = 0.5,right = 1.2,top = 1.2)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
xy_high = density_rgb("./pics/01-Xylella-tobacco-bg-white/82.jpg",
                       limiar = 200, index_cut = "Blue",
                      left =0.5,bottom = 0.5,right = 1.2,top = 1.2)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
xy_low+xy_high

WLB

wlb_low = density_rgb("./pics/01-Wheat_leaf_blast/G_108_R3.jpg",
                       limiar = 180, index_cut = "Blue")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
wlb_high = density_rgb("./pics/01-Wheat_leaf_blast/T_239_R1.jpg",
                       limiar = 180, index_cut = "Blue")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
wlb_low+wlb_high

PLB

plb_low = density_rgb("./pics/01-potato_late_bligh/PI24_6B.png",
                       limiar = 1, index_cut = "Red", cropAbove = F,
                      0.55,0.55,1.2,1.1)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Red"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
plb_high = density_rgb("./pics/01-potato_late_bligh/PI07_2A.png",
                       limiar = 1, index_cut = "Red", cropAbove = F,
                      0.55,0.55,1.2,1.1)
## [1] "3 layers available"
## [1] "Mask equation myIndex=Red"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
plb_low+plb_high

## COMBO RGB

tags = c("A", "", "B", "", "C", "","D","","E","","F","","G","","H","","I","","J","")
SBR_low+SBR_high+
  calo_low+calo_high+
  xy_low+xy_high+
  wlb_low+wlb_high+
  plb_low+plb_high+
  plot_layout(widths = c(1, 1),
               heights = c(1,1,1,1,1),
              tag_level = "keep",
              guides = 'collect')+
  plot_annotation(tag_levels = list(tags))&
  theme(legend.key.size = unit(5, 'mm'),
        legend.position = "bottom",
        legend.text = element_text(size =10))

ggsave("figs/RGB_dens.png",dpi = 600, height = 8, width =7)

new

density_rgb2 = function(
file_low = "./pics/01-soybean-rust-bg-blue/Ferrugem 52_Median.jpg",
file_high = "./pics/01-soybean-rust-bg-blue/Ferrugem 49_Median.jpg",
limiar = 100,
index_cut = "Blue",
cropAbove=T,
title = "Soybean Rust",face = "plain"){

#-------------------------------------------------------------------------------------------------
SBR_low_EX.L1<-stack(paste(file_low ))
SBR_low_EX.L1<-aggregate(SBR_low_EX.L1, fact=5)

SBR_low_EX.L2<-fieldMask(mosaic=SBR_low_EX.L1, myIndex = c(index_cut), cropValue=limiar, cropAbove=cropAbove, plot = F)

cut = mask(SBR_low_EX.L1, SBR_low_EX.L2$newMosaic)
SBR_low_EX.L4<-fieldIndex(mosaic=cut,
                  # index =index,
                  plot =F)

SBR_low = RStoolbox::ggRGB(SBR_low_EX.L2$newMosaic,r = 1,g = 2,b = 3)+
  theme_map()+coord_fixed()+
  theme(panel.background = element_rect(color = NA, fill = NA),
        plot.title = element_text(size=8, face = "plain"))+
  labs(title = "Low")

SBR_low_comb = data.frame(R = as.data.frame(SBR_low_EX.L4$Red),
           G = as.data.frame(SBR_low_EX.L4$Blue),
           B = as.data.frame(SBR_low_EX.L4$Green)) %>%
  na.omit() %>% 
  pivot_longer(1:3,names_to = "band", values_to = "value") %>%
  mutate(sev="Low")
#-------------------------------------------------------------------------------------------------

SBR_high_EX.L1<-stack(paste(file_high))
SBR_high_EX.L1<-aggregate(SBR_high_EX.L1, fact=5)

SBR_high_EX.L2<-fieldMask(mosaic=SBR_high_EX.L1,  myIndex = c(index_cut), cropValue=limiar, cropAbove=cropAbove, plot = F)

cut = mask(SBR_high_EX.L1, SBR_high_EX.L2$newMosaic)
SBR_high_EX.L4<-fieldIndex(mosaic=cut,
                  # index =index,
                  plot =F)

SBR_high = RStoolbox::ggRGB(SBR_high_EX.L2$newMosaic,r = 1,g = 2,b = 3)+
  theme_map()+coord_fixed()+
  theme(panel.background = element_rect(color = NA, fill = NA),
        plot.title = element_text(size=8, face = "plain"))+
  labs(title = "High")

SBR_high_comb = data.frame(R = as.data.frame(SBR_high_EX.L4$Red),
           G = as.data.frame(SBR_high_EX.L4$Blue),
           B = as.data.frame(SBR_high_EX.L4$Green)) %>%
  na.omit() %>% 
  pivot_longer(1:3,names_to = "band", values_to = "value") %>%
  mutate(sev="High")

#-------------------------------------------------------------------------------------------------
all_comb = bind_rows(SBR_low_comb,SBR_high_comb) %>% 
  mutate(sev =factor(sev, levels =c("Low","High")))
#-------------------------------------------------------------------------------------------------

all_comb %>% 
  ggplot(aes(value,sev))+
  stat_slab(aes(fill = band), alpha = 0.7)+
   stat_pointinterval(aes(color = band),
                      position = position_dodge(width = .5, preserve = "single"),
                     # color = "gray40",
                     .width = c(0,0.95))+
  
  scale_fill_manual(values = c("blue", "green","red" ))+
  scale_color_manual(values = c("blue", "green","red" ))+
  theme_minimal()+
  xlim(0,255)+
  theme(panel.grid = element_blank(),
        plot.title = element_text(size = 10, face = face),
        axis.ticks = element_line(color = "gray"),
        axis.line = element_line(color = "gray"))+
  labs(x = "Pixel intensity",
       y = "Severity",
       fill ="",
       title = paste(title))+  
  guides(color =F)#+
  #SBR_low+SBR_high+
  #plot_layout(widths = c(1, .2,.2))
}

plots

SBR_dist = density_rgb2()
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
calo_dist =density_rgb2(file_low ="./pics/01-Calonectria_leaf_bligth/108.jpg",
                        file_high = "./pics/01-Calonectria_leaf_bligth/153.jpg",
                        limiar = 175,index_cut = "Blue",cropAbove=T,
                        title = "Calonectria leaf blight")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
xy_dist = density_rgb2(file_low ="./pics/01-Xylella-tobacco-bg-white/68.jpg",
                        file_high = "./pics/01-Xylella-tobacco-bg-white/82.jpg",
                        limiar = 200,index_cut = "Blue", cropAbove=T,
                        title = "N. tabacum-X. fastidiosa", face = "italic")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
wlb_dist = density_rgb2(file_low ="./pics/01-Wheat_leaf_blast/G_108_R3.jpg",
                        file_high = "./pics/01-Wheat_leaf_blast/T_239_R1.jpg",
                        limiar = 180,index_cut = "Blue",cropAbove=T,
                        title = "Wheat leaf blast")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
## [1] "3 layers available"
## [1] "Mask equation myIndex=Blue"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
plb_dist = density_rgb2(file_low ="./pics/01-potato_late_bligh/PI24_6B.png",
                        file_high = "./pics/01-potato_late_bligh/PI07_2A.png",
                        limiar = 1,index_cut = "Red",cropAbove=F,
                        title = "Potato late blight")
## [1] "3 layers available"
## [1] "Mask equation myIndex=Red"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.
## [1] "3 layers available"
## [1] "Mask equation myIndex=Red"
## [1] "3 layers available"
## Coordinate system already present. Adding new coordinate system, which will replace the existing one.

combo

(SBR_dist+calo_dist+xy_dist+wlb_dist+plb_dist+guide_area())+
  plot_layout(nrow = 3,
              ncol = 2,
              tag_level = "keep",
              # widths = c(1,1,1,1,1),
              guides = 'collect')+
  plot_annotation(tag_levels = "A")+
  # plot_annotation(tag_levels = list(tags2))&
  theme(legend.key.size = unit(5, 'mm'),
        legend.position = "none",
        legend.text = element_text(size =10))

ggsave("figs/RGB_dens2.png",dpi = 600, height = 7, width =6)